BarrenPlateaus_EN.ipynb

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    "# Barren Plateaus\n",
    "\n",
    "<em> Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. </em>"
   ]
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    "## Overview\n",
    "\n",
    "In the training of classical neural networks, gradient-based optimization methods encounter the problem of local minimum and saddle points. Correspondingly, the Barren plateau phenomenon could potentially block us from efficiently training quantum neural networks. This peculiar phenomenon was first discovered by McClean et al. in 2018 [[1]](https://arxiv.org/abs/1803.11173). In a few words, when we randomly initialize the parameters in random circuit structure meets a certain degree of complexity, the optimization landscape will become very flat, which makes it difficult for the optimization method based on gradient descent to find the global minimum. For most variational quantum algorithms (VQE, etc.), this phenomenon means that when the number of qubits increases, randomly choosing a circuit ansatz and randomly initializing the parameters of it may not be a good idea. This will make the optimization landscape corresponding to the loss function into a huge plateau, which makes the training of QNN much more difficult. The initial random value for the optimization process is very likely to stay inside this plateau, and the convergence time of gradient descent will be prolonged.\n",
    "\n",
    "![BP-fig-barren](./figures/BP-fig-barren.png)\n",
    "\n",
    "The figure is generated through [Gradient Descent Viz](https://github.com/lilipads/gradient_descent_viz)\n",
    "\n",
    "Based on the impact of gradient variation on the training of such variational quantum algorithms, we provide a gradient analysis tool module in the Paddle Quantum to assist users in diagnosing models and facilitate the study of problems such as barren plateaus.\n",
    "\n",
    "This tutorial mainly discusses how to demonstrate the barren plateau phenomenon with Paddle Quantum and use the gradient analysis tool to analyze the parameter gradients in user-defined quantum neural networks. Although it does not involve any algorithmic innovation, it can help readers to understand the gradient-based training for QNN.\n",
    "\n",
    "We first import the necessary libraries and packages:\n"
   ]
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      "c:\\Users\\jingmingrui\\Anaconda3\\envs\\pd_dep\\lib\\site-packages\\openfermion\\hamiltonians\\hartree_fock.py:11: DeprecationWarning: Please use `OptimizeResult` from the `scipy.optimize` namespace, the `scipy.optimize.optimize` namespace is deprecated.\n",
      "  from scipy.optimize.optimize import OptimizeResult\n"
     ]
    }
   ],
   "source": [
    "# ignore waring \n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "# Import packages needed\n",
    "import time\n",
    "import numpy as np\n",
    "from math import pi\n",
    "import paddle\n",
    "from paddle_quantum.state import zero_state\n",
    "from paddle_quantum.ansatz import Circuit\n",
    "from paddle_quantum.linalg import dagger\n",
    "\n",
    "# Drawing tools\n",
    "from matplotlib import pyplot as plt "
   ]
  },
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   "source": [
    "## Random network structure\n",
    "\n",
    "Here we follow the original method mentioned in the paper by McClean (2018) [[1]](https://arxiv.org/abs/1803.11173) and build the following random circuit:\n",
    "\n",
    "![BP-fig-Barren_circuit](./figures/BP-fig-Barren_circuit.png)\n",
    "\n",
    "First, we rotate all the qubits around the $y$-axis of the Bloch sphere with rotation gates $R_y(\\pi/4)$.\n",
    "\n",
    "The remaining structure is in form of blocks, each block can be further divided into two layers:\n",
    "\n",
    "- The first layer is a set of random rotation gates on all the qubits, where $R_{\\ell,n} \\in \\{R_x, R_y, R_z\\}$. The subscript $\\ell$ means the gate is in the $\\ell$-th repeated block. In the figure above, $\\ell =1$. The second subscript $n$ indicates which qubit it acts on.\n",
    "- The second layer is composed of CZ gates, which act on adjacent qubits.\n",
    "\n",
    "In Paddle Quantum, we can build this circuit with the following code:"
   ]
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    "def rand_circuit(theta, target, num_qubits):\n",
    "    # Initialize the quantum circuit\n",
    "    cir = Circuit(num_qubits)\n",
    "    \n",
    "    # Fixed-angle Ry rotation gates \n",
    "    cir.ry(param=pi / 4)\n",
    "\n",
    "    # ============== First layer ==============\n",
    "    # Fixed-angle Ry rotation gates \n",
    "    for i in range(num_qubits):\n",
    "        if target[i] == 0:\n",
    "            cir.rz(i, param=theta[i])\n",
    "        elif target[i] == 1:\n",
    "            cir.ry(i, param=theta[i])\n",
    "        else:\n",
    "            cir.rx(i, param=theta[i])\n",
    "            \n",
    "    # ============== Second layer ==============\n",
    "    # Build adjacent CZ gates\n",
    "    for i in range(num_qubits - 1):\n",
    "        cir.cz([i, i + 1])\n",
    "        \n",
    "    return cir"
   ]
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   "source": [
    "## Loss function and optimization landscape\n",
    "\n",
    "After determining the circuit structure, we also need to define a loss function to determine the optimization landscape. Following the same set up with McClean (2018)[[1]](https://arxiv.org/abs/1803.11173), we take the loss function from VQE:\n",
    "\n",
    "$$\n",
    "\\mathcal{L}(\\boldsymbol{\\theta})= \\langle0| U^{\\dagger}(\\boldsymbol{\\theta})H U(\\boldsymbol{\\theta}) |0\\rangle,\n",
    "\\tag{1}\n",
    "$$\n",
    "\n",
    "The unitary matrix $U(\\boldsymbol{\\theta})$ is the quantum neural network with the random structure that we build from the last section. For the Hamiltonian $H$, we also take the simplest form $H = |00\\cdots 0\\rangle\\langle00\\cdots 0|$. After that, we can start sampling gradients with the two-qubit case - generate 300 sets of random network structures and different random initial parameters $\\{\\theta_{\\ell,n}^{( i)}\\}_{i=1}^{300}$. Each time the partial derivative with respect to the **first parameter $\\theta_{1,1}$** is calculated according to the analytical gradient formula from VQE. Then we analyze the mean and variance of these 300 sampled partial gradients. The formula for the analytical gradient is:\n",
    "\n",
    "$$\n",
    "\\partial \\theta_{j} \n",
    "\\equiv \\frac{\\partial \\mathcal{L}}{\\partial \\theta_j}\n",
    "= \\frac{1}{2} \\big[\\mathcal{L}(\\theta_j + \\frac{\\pi}{2}) - \\mathcal{L}(\\theta_j - \\frac{\\pi}{2})\\big].\n",
    "\\tag{2}\n",
    "$$\n",
    "\n",
    "For a detailed derivation, see [arXiv:1803.00745](https://arxiv.org/abs/1803.00745).\n"
   ]
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      "c:\\Users\\jingmingrui\\Anaconda3\\envs\\pd_dep\\lib\\site-packages\\paddle\\fluid\\framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  elif dtype == np.bool:\n",
      "c:\\Users\\jingmingrui\\Anaconda3\\envs\\pd_dep\\lib\\site-packages\\paddle\\tensor\\creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if data.dtype == np.object:\n"
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     "text": [
      "The main program segment has run in total  3.090050458908081  seconds\n",
      "Use  300  samples to get the mean value of the gradient of the random network's first parameter, and we have： 0.016533764\n",
      "Use  300 samples to get the variance of the gradient of the random network's first parameter, and we have： 0.09683221\n"
     ]
    }
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   "source": [
    "# Hyper parameter settings\n",
    "# np.random.seed(42)   # Fixed Numpy random seed\n",
    "N = 2                # Set the number of qubits\n",
    "samples = 300        # Set the number of sampled random network structures\n",
    "THETA_SIZE = N       # Set the size of the parameter theta\n",
    "ITR = 1              # Set the number of iterations\n",
    "LR = 0.2             # Set the learning rate\n",
    "SEED = 1             # Fixed the randomly initialized seed in the optimizer\n",
    "\n",
    "# Initialize the register for the gradient value\n",
    "grad_info = []\n",
    "\n",
    "# paddle.seed(SEED)\n",
    "class manual_gradient(paddle.nn.Layer):\n",
    "    \n",
    "    # Initialize a list of learnable parameters and fill the initial value with a uniform distribution of [0, 2*pi]\n",
    "    def __init__(self, shape, param_attr=paddle.nn.initializer.Uniform(low=0.0, high=2 * pi), dtype='float32'):\n",
    "        super(manual_gradient, self).__init__()\n",
    "        \n",
    "        # Convert Numpy array to Tensor in PaddlePaddle\n",
    "        self.H = zero_state(N).data\n",
    "        \n",
    "    # Define loss function and forward propagation mechanism  \n",
    "    def forward(self):\n",
    "        \n",
    "        # Initialize three theta parameter lists\n",
    "        theta_np = np.random.uniform(low=0., high= 2 * pi, size=(THETA_SIZE))\n",
    "        theta_plus_np = np.copy(theta_np) \n",
    "        theta_minus_np = np.copy(theta_np) \n",
    "        \n",
    "        # Modified to calculate analytical gradient\n",
    "        theta_plus_np[0] += np.pi/2\n",
    "        theta_minus_np[0] -= np.pi/2\n",
    "        \n",
    "        # Convert Numpy array to Tensor in PaddlePaddle\n",
    "        theta_plus = paddle.to_tensor(theta_plus_np)\n",
    "        theta_minus = paddle.to_tensor(theta_minus_np)\n",
    "        \n",
    "        # Generate random targets, randomly select circuit gates in rand_circuit\n",
    "        target = np.random.choice(3, N)      \n",
    "        \n",
    "        U_plus = rand_circuit(theta_plus, target, N).unitary_matrix()\n",
    "        U_minus = rand_circuit(theta_minus, target, N).unitary_matrix()\n",
    "\n",
    "        # Calculate the analytical gradient\n",
    "        grad = paddle.real((dagger(U_plus) @ self.H @ U_plus)[0][0] - (dagger(U_minus) @ self.H @ U_minus)[0][0])/2  \n",
    "\n",
    "        return grad\n",
    "\n",
    "# Define the main block\n",
    "def main():\n",
    "\n",
    "    # Set the dimension of QNN\n",
    "    sampling = manual_gradient(shape=[THETA_SIZE])\n",
    "        \n",
    "    # Sampling to obtain gradient information\n",
    "    grad = sampling().numpy()\n",
    "        \n",
    "    return grad\n",
    "\n",
    "# Record running time\n",
    "time_start = time.time()\n",
    "\n",
    "# Start sampling\n",
    "for i in range(samples):\n",
    "    if __name__ == '__main__':\n",
    "        grad = main()\n",
    "        grad_info.append(grad)\n",
    "\n",
    "time_span = time.time() - time_start\n",
    "\n",
    "print('The main program segment has run in total ', time_span, ' seconds')\n",
    "print(\"Use \", samples, \" samples to get the mean value of the gradient of the random network's first parameter, and we have：\", np.mean(grad_info))\n",
    "print(\"Use \", samples, \"samples to get the variance of the gradient of the random network's first parameter, and we have：\", np.var(grad_info))"
   ]
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    "## Visualization of the Optimization landscape\n",
    "\n",
    "Next, we use Matplotlib to visualize the optimization landscape. In the case of **two qubits**, we only have two parameters $\\theta_1$ and $\\theta_2$, and there are 9 possibilities for the random circuit structure in the second layer. \n",
    "\n",
    "![BP-fig-landscape2](./figures/BP-fig-landscape2.png)\n",
    "\n",
    "The plain structure shown in the $R_z$-$R_z$ layer from the last figure is something we should avoid. In this case, it's nearly impossible to converge to the theoretical minimum. If you want to try to draw some optimization landscapes yourself, please refer to the following code:"
   ]
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",
      "text/plain": [
       "<Figure size 1152x345.6 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The main program segment has run in total  1.7086431980133057  seconds\n"
     ]
    }
   ],
   "source": [
    "time_start = time.time()\n",
    "N = 2\n",
    "\n",
    "# Set the image ratio Vertical: Horizontal = 0.3\n",
    "fig = plt.figure(figsize=plt.figaspect(0.3))\n",
    "\n",
    "# Generate points on the x, y axis\n",
    "X = np.linspace(0, 2 * np.pi, 80)\n",
    "Y = np.linspace(0, 2 * np.pi, 80)\n",
    "\n",
    "# Generate 2D mesh\n",
    "xx, yy = np.meshgrid(X, Y)\n",
    "\n",
    "\n",
    "# Define the necessary logic gates\n",
    "def rx(theta):\n",
    "    mat = np.array([[np.cos(theta/2), -1j * np.sin(theta/2)],\n",
    "                    [-1j * np.sin(theta/2), np.cos(theta/2)]])\n",
    "    return mat\n",
    "\n",
    "def ry(theta):\n",
    "    mat = np.array([[np.cos(theta/2), -1 * np.sin(theta/2)],\n",
    "                    [np.sin(theta/2), np.cos(theta/2)]])\n",
    "    return mat\n",
    "\n",
    "def rz(theta):\n",
    "    mat = np.array([[np.exp(-1j * theta/2), 0],\n",
    "                    [0, np.exp(1j * theta/2)]])\n",
    "    return mat\n",
    "\n",
    "def CZ():\n",
    "    mat = np.array([[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,-1]])\n",
    "    return mat\n",
    "\n",
    "# ============= The first figure =============\n",
    "# We visualize the case where the second layer is kron(Ry, Ry)\n",
    "ax = fig.add_subplot(1, 2, 1, projection='3d')\n",
    "\n",
    "# Forward propagation to calculate loss function:\n",
    "def cost_yy(para):\n",
    "    L1 = np.kron(ry(np.pi/4), ry(np.pi/4))\n",
    "    L2 = np.kron(ry(para[0]), ry(para[1]))\n",
    "    U = np.matmul(np.matmul(L1, L2), CZ())\n",
    "    H = np.zeros((2 ** N, 2 ** N))\n",
    "    H[0, 0] = 1\n",
    "    val = (U.conj().T @ H@ U).real[0][0]\n",
    "    return val\n",
    "\n",
    "# Draw an image\n",
    "Z = np.array([[cost_yy([x, y]) for x in X] for y in Y]).reshape(len(Y), len(X))\n",
    "surf = ax.plot_surface(xx, yy, Z, cmap='plasma')\n",
    "ax.set_xlabel(r\"$\\theta_1$\")\n",
    "ax.set_ylabel(r\"$\\theta_2$\")\n",
    "ax.set_title(\"Optimization Landscape for Ry-Ry Layer\")\n",
    "\n",
    "# ============= The second figure =============\n",
    "# We visualize the case where the second layer is kron(Rx, Rz)\n",
    "ax = fig.add_subplot(1, 2, 2, projection='3d')\n",
    "\n",
    "\n",
    "def cost_xz(para):\n",
    "    L1 = np.kron(ry(np.pi/4), ry(np.pi/4))\n",
    "    L2 = np.kron(rx(para[0]), rz(para[1]))\n",
    "    U = np.matmul(np.matmul(L1, L2), CZ())\n",
    "    H = np.zeros((2 ** N, 2 ** N))\n",
    "    H[0, 0] = 1\n",
    "    val = (U.conj().T @ H @ U).real[0][0]\n",
    "    return val\n",
    "\n",
    "Z = np.array([[cost_xz([x, y]) for x in X] for y in Y]).reshape(len(Y), len(X))\n",
    "surf = ax.plot_surface(xx, yy, Z, cmap='viridis')\n",
    "ax.set_xlabel(r\"$\\theta_1$\")\n",
    "ax.set_ylabel(r\"$\\theta_2$\")\n",
    "ax.set_title(\"Optimization Landscape for Rx-Rz Layer\")\n",
    "\n",
    "\n",
    "plt.show()\n",
    "\n",
    "time_span = time.time() - time_start        \n",
    "print('The main program segment has run in total ', time_span, ' seconds')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gradient Analysis Tool\n",
    "\n",
    "Based on an important role that gradients play in phenomena such as barren plateaus, we developed a simple gradient analysis tool in Paddle Quantum to assist users in viewing gradients of each parameter in the circuit. This tool can be used to facilitate subsequent research on quantum neural networks.\n",
    "\n",
    "Note that the users only need to define the **circuit** and **loss function** separately when using the gradient analysis tool, and there is no need to write their networks.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Application I: Unsupervised Learning\n",
    "\n",
    "For this case, we focus on variational quantum algorithms similar to the Variational Quantum Eigensolver (VQE). Suppose the objective function is the typical parameterized cost function used in VQA: $O(\\theta) = \\left\\langle0\\dots 0\\right\\lvert U^{\\dagger}(\\theta)HU(\\theta) \\left\\lvert0\\dots 0\\right\\rangle$，where $U(\\theta)$ is a parameterized quantum circuit, $H$ is a Hamiltonian and $\\theta = [\\theta_1, \\theta_2, \\dots, \\theta_n]$ is a list of trainable parameters in the circuit.\n",
    "\n",
    "Here we use VQE to demonstrate the usage of this gradient analysis tool.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Paddle Quantum Implement\n",
    "\n",
    "Firstly, import the packages needed for the problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import related modules from Paddle Quantum and PaddlePaddle\n",
    "from paddle_quantum.qinfo import pauli_str_to_matrix, random_pauli_str_generator\n",
    "from paddle_quantum.hamiltonian import Hamiltonian\n",
    "# GradTool package\n",
    "from paddle_quantum.gradtool import random_sample, show_gradient, plot_loss_grad, show_gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Define Quantum Circuits\n",
    "\n",
    "Next, construct the parameterized quantum circuit $U(\\theta)$ in the objective function. Here we still use the random circuit defined above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Define Objective Function\n",
    "\n",
    "Note here that in the gradient analysis module we call the function in the form of ``loss_func(circuit, *args)`` to calculate the objective function value. This means that the second argument is a variable argument, and the user is able to construct their own objective function form as needed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# objective function\n",
    "def loss_func(circuit: Circuit, H: Hamiltonian) -> paddle.Tensor:\n",
    "    return circuit().expec_val(H, shots = 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then set some parameters required for the application."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Hyper parameter settings\n",
    "np.random.seed(42)   # Fixed Numpy random seed\n",
    "N = 2                # Set the number of qubits\n",
    "samples = 300        # Set the number of sampled random network structures\n",
    "THETA_SIZE = N       # Set the size of the parameter theta\n",
    "ITR = 120            # Set the number of iterations\n",
    "LR = 0.1             # Set the learning rate\n",
    "SEED = 1             # Fixed the randomly initialized seed in the optimizer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Randomly generate quantum circuits and a list of Hamiltonian information."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--Ry(0.785)----Rx(1.077)----*--\n",
      "                            |  \n",
      "--Ry(0.785)----Rz(0.623)----z--\n",
      "                               \n",
      "Hamiltonian info:  -0.6880109593275947 Z1\n",
      "0.7323522915498704 Z0\n",
      "-0.8871768419457995 Y0, Y1\n",
      "-0.7724600283015672 X1\n",
      "-0.39151551408092455 Y1\n",
      "0.22370578944475894 Y0, Z1\n"
     ]
    }
   ],
   "source": [
    "# paddle.seed(SEED)\n",
    "target = np.random.choice(3, N)\n",
    "# Random generate parameters between 0 and 2*Pi \n",
    "theta = paddle.rand([THETA_SIZE]).astype('float32') * 2 * pi\n",
    "theta.stop_gradient = False\n",
    "cir = rand_circuit(theta, target, N)\n",
    "print(cir)\n",
    "# Random generate Hamiltonian information, in Pauli string format\n",
    "H_l = Hamiltonian(random_pauli_str_generator(N, terms=7))\n",
    "print('Hamiltonian info: ', H_l)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "``cir`` and ``H_l`` are the parameters needed for the objective function ``loss_func``."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the gradient analysis tool, we can get the results of the gradient sampling of each parameter in the circuit. There are three modes ``single``, ``max``, and ``random`` for users to choose, where ``single`` returns the mean and variance of each parameter after sampling the circuit multiple times, ``max`` mode returns the mean and variance of the maximum value of all parameter gradients in each round, and ``random`` calculates the mean and variance of random value of all parameter gradients in each round.\n",
    "\n",
    "We sample the circuit 300 times, and here we choose the ``single`` mode to see the mean and variance of the gradient of each variable parameter in the circuit, while the default ``param=0`` means plot gradient distribution of the first parameter.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: 100%|###################################################| 300/300 [00:03<00:00, 77.68it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean of gradient for all parameters: \n",
      "theta 1 :  0.015548194\n",
      "theta 2 :  -0.026560133\n",
      "Variance of gradient for all parameters: \n",
      "theta 1 :  0.20417707\n",
      "theta 2 :  0.13769649\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "grad_mean_list, grad_variance_list = random_sample(cir, loss_func, samples, H_l, mode='single', param=0)       "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The user can also use the ``plot_loss_grad`` function to show the gradient and loss values variation during the training process."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Training:   0%|                                                             | 0/120 [00:00<?, ?it/s]c:\\Users\\jingmingrui\\Anaconda3\\envs\\pd_dep\\lib\\site-packages\\paddle\\fluid\\framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  elif dtype == np.bool:\n",
      "c:\\Users\\jingmingrui\\Anaconda3\\envs\\pd_dep\\lib\\site-packages\\paddle\\tensor\\creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if data.dtype == np.object:\n",
      "Training: 100%|###################################################| 120/120 [00:01<00:00, 89.18it/s]\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_loss_grad(cir, loss_func, ITR, LR, H_l)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As shown above, the loss value does not change after a few dozen times, and the gradient is very close to 0.\n",
    "In order to see the difference between the optimal solution and the theoretical value clearly, we calculate the eigenvalues of the Hamiltonian ``H_l``."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Training: 100%|###################################################| 120/120 [00:01<00:00, 87.80it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "optimal result:  -1.2294903\n",
      "real energy： -2.064555\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "loss, grad = show_gradient(cir, loss_func, ITR, LR, H_l)\n",
    "H_matrix = H_l.construct_h_matrix()\n",
    "\n",
    "print(\"optimal result: \", loss[-1])\n",
    "print(\"real energy：\", np.linalg.eigh(H_matrix)[0][0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The comparison shows that there is still a gap between the optimal solution obtained from the training of this circuit and the actual value."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### More qubits\n",
    "\n",
    "Since in the barren plateau effect, the gradient disappears exponentially with increasing the number of quantum bits. Then, we will see what happens to the sampled gradients when we increase the number of qubits(here we sample by choosing ``max`` mode)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: 100%|###################################################| 300/300 [00:03<00:00, 75.81it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean of max gradient\n",
      "0.72318614\n",
      "Variance of max gradient\n",
      "0.0966615\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling:   0%|                                                             | 0/300 [00:00<?, ?it/s]c:\\Users\\jingmingrui\\Anaconda3\\envs\\pd_dep\\lib\\site-packages\\paddle\\fluid\\framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  elif dtype == np.bool:\n",
      "c:\\Users\\jingmingrui\\Anaconda3\\envs\\pd_dep\\lib\\site-packages\\paddle\\tensor\\creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if data.dtype == np.object:\n",
      "Sampling: 100%|###################################################| 300/300 [00:06<00:00, 42.95it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean of max gradient\n",
      "0.6837325\n",
      "Variance of max gradient\n",
      "0.0811426\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling:   0%|                                                             | 0/300 [00:00<?, ?it/s]c:\\Users\\jingmingrui\\Anaconda3\\envs\\pd_dep\\lib\\site-packages\\paddle\\fluid\\framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  elif dtype == np.bool:\n",
      "c:\\Users\\jingmingrui\\Anaconda3\\envs\\pd_dep\\lib\\site-packages\\paddle\\tensor\\creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if data.dtype == np.object:\n",
      "Sampling: 100%|###################################################| 300/300 [00:10<00:00, 29.67it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean of max gradient\n",
      "0.31329232\n",
      "Variance of max gradient\n",
      "0.01599442\n"
     ]
    },
    {
     "data": {
      "image/png": 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ZDXGtXhF8A7hT0g1p/k+Br1USkZmZDaqWEkFE/LukW4F3pUUnR8Q9lUVlZmaDpmkikDQ2Ip6VtAuwMj261+0SEU9XG56ZmVWttyuCq4H3A3cBUVquNL93RXGZmdkgaZoIIuL96e9egxOOmZkNtla/R3BzK8vMzGzo6W2MYAywHTBO0s5s+sjoWDb/kRkzMxuCehsjOB34G2A8xThBdyJ4FriourDMzGyw9DZGcAFwgaSPR4S/RWxmNgy1+j2CL0vaH5gCjCktv6KqwMzMbHC0lAgkfZbil8SmUPy+wHTgNsCJwMxsiGv1XkPHAYcDT0TEycBbgR0ri8rMzAZNq4lgQ0T8AdgoaSzwJD1/mN7MzIaoXruGJAm4T9JOwGUUnx56nuI21GZmNsT1mggiIiRNjYhngEsk/RAYGxH3VR6dmZlVrtWuobslHQwQESudBMzMho9Wf4/gEOBDkh4FXiDddC4iDqgsMjMzGxStJoIjK43CzMzaptUvlD1adSBmZtYerY4RmJnZMOVEYGaWOScCM7PMORGYmWXOicDMLHNOBGZmmXMiMDPLnBOBmVnmKk0Eko6StEzScklzmpT7C0khqbPKeMzMbHOVJQJJI4CLKX7NbAowS9KUOuV2AD4J3FlVLGZm1liVVwRTgeURsSIiXgauBWbUKfevwHnAhgpjMTOzBqpMBBOAVaX51WnZayQdBOwREd9vVpGk0yQtlrS4q6tr4CM1M8tY2waLJb0O+Hfg072VjYhLI6IzIjo7OjqqD87MLCNVJoI19Pxd44lpWbcdgP2BWyWtBA4F5nvA2MxscFWZCBYBkyXtJWkUMBOY370yItZHxLiImBQRk4A7gGMjYnGFMZmZWY3KEkFEbARmAwuBB4B5EbFE0lxJx1a1XTMz65tWf6GsXyJiAbCgZtnZDcpOqzIWMzOrz98sNjPLnBOBmVnmnAjMzDLnRGBmljknAjOzzDkRmJllzonAzCxzTgRmZplzIjAzy5wTgZlZ5pwIzMwy50RgZpY5JwIzs8w5EZiZZc6JwMwsc04EZmaZcyIwM8ucE4GZWeacCMzMMudEYGaWOScCM7PMORGYmWXOicDMLHNOBGZmmXMiMDPLnBOBmVnmnAjMzDLnRGBmljknAjOzzDkRmJllzonAzCxzTgRmZplzIjAzy1yliUDSUZKWSVouaU6d9Z+StFTSfZJulrRnlfGYmdnmKksEkkYAFwPTgSnALElTaordA3RGxAHAt4EvVhWPmZnVV+UVwVRgeUSsiIiXgWuBGeUCEXFLRLyYZu8AJlYYj5mZ1VFlIpgArCrNr07LGjkV+EG9FZJOk7RY0uKurq4BDNHMzLaKwWJJHwY6gS/VWx8Rl0ZEZ0R0dnR0DG5wZmbD3MgK614D7FGan5iW9SDpCOAs4N0R8VKF8ZiZWR1VXhEsAiZL2kvSKGAmML9cQNKBwFeAYyPiyQpjMTOzBipLBBGxEZgNLAQeAOZFxBJJcyUdm4p9CXg9cL2kX0ma36A6MzOrSJVdQ0TEAmBBzbKzS9NHVLl9MzPr3VYxWGxmZu3jRGBmljknAjOzzDkRmJllzonAzCxzTgRmZplzIjAzy5wTgZlZ5pwIzMwy50RgZpY5JwIzs8w5EZiZZc6JwMwsc04EZmaZcyIwM8ucE4GZWeacCMzMMudEYGaWOScCM7PMORGYmWXOicDMLHNOBGZmmXMiMDPLnBOBmVnmnAjMzDLnRGBmljknAjOzzDkRmJllzonAzCxzTgRmZplzIjAzy5wTgZlZ5pwIzMwyV2kikHSUpGWSlkuaU2f9aEnXpfV3SppUZTxmZra5kVVVLGkEcDHwXmA1sEjS/IhYWip2KrAuIv5I0kzgPOD4qmIys9ZMmvP9docAwMovHNPuELJQ5RXBVGB5RKyIiJeBa4EZNWVmAN9M098GDpekCmMyM7MalV0RABOAVaX51cAhjcpExEZJ64FdgafKhSSdBpyWZp+XtKySiFszjpr4Muf22MRt0dMWt4fOG6BItg7tbo89G62oMhEMmIi4FLi03XEASFocEZ3tjmNr4fbYxG3Rk9ujp625ParsGloD7FGan5iW1S0jaSSwI7C2wpjMzKxGlYlgETBZ0l6SRgEzgfk1ZeYDJ6bp44CfRERUGJOZmdWorGso9fnPBhYCI4CvR8QSSXOBxRExH/gacKWk5cDTFMlia7dVdFFtRdwem7gtenJ79LTVtof8BtzMLG/+ZrGZWeacCMzMMpd9IkiD2Xem21xclwa265U7M5VZJunI0vK6t9FoVK+k/y7pbkkbJR3Xz5gl6SeSxjaLoeY5DW/n0Y99m52WhaRxTeKsW29NmUbtVDdeSbtKukXS85Iuqqnrx5J2Ls1vK+m/JI2QdKKkh9LjROqQtIukH6UyP+quK7X3hSmW+yQdVHrODyU9I+nGJu1Qt9465erGKOlcSaskPV9TfrakUxptt1UD2E77SvqFpJckfabJ9v5E0q9Te14obf4l0kZ1SRol6acqPmW41Wt0fNeUaXhMD5qIyO4BjAK2T9PzgJlp+hLgf9QpPwW4FxgN7AU8TDEAPiJN753qvBeY0qxeYBJwAHAFcFw/4z8G+I803TCGmuf8T+CSND0TuG4L9u3AtB8rgXENYqxbb51yjdqpUbzbA+8CzgAuqqnrROCs0vzHgE8CuwAr0t+d0/TOdWL5IjAnTc8BzkvTRwM/AAQcCtxZes7hwAeAG5u8XnXrrSnTMMa0zd2B52uesx1wzwD8PwxUO+0GHAycC3ymyfZ+mfZJqV2n1ynTsC7gs8CHBvq80M+226x9Wjm+a8o0PKYHbT/a3ZCD/KLtB5wPPEJxMhPFN/1GpvVvBxbWed6ZwJml+YWpbI/y3eVaqRe4nP4ngquBafXqro21NuY0PTLFp77uW02dK2mcCOrWW1OmYTs1irf03JNq/2nSyev+0vzPKRLWLOArpeVfAWbViXkZsHua3h1YVq98uVyan0bzRFC33poyvcZITSJIy24Apm7h/8WAtFNp/Tk0SASp/G8a7Xed8pvVBbwVWLAl+zxQD4o3ON8C3lM+Pns7vhvUtdkxPViPYd81JGl7SSdLug24DFgKHBAR91DczuKZiNiYiq+muO1FrXq3y5jQZHmr9fbXO4G7eomtVo/beQDdt/Po6761qpXnN2unRvE2FBHrgNHpUnsUsHdErOzDvrwhIh5P008Ab+jDvjTTqN6y/m5jMXBYH2LpYYDbqRUTUr29baOZ+ymuFrYG+wDXALOBpZL+UdL4tK7q88CAGRL9bFvoceA+4CMR8Zt2BzNAdomI59odxFbqSWA8xTfUn+lvJRERkgb8s9UV1PsksO8WPH8cW2E79bLNVyW9LGmHdv8fRMSrwI3AjZI6gM8Dv5X0DoqutSFh2F8RUHxjeQ3wXUlnSyrfeGktsFNp4KnebTCg8e0yGi1vtd7+2iip+7Vr5VYePcqp5+08+rpvrWrl+c3aqb+3HxkD/D49xvQhFoDfSdo9bXN3ipNsX57fSKN6y/q7je797a+BbKdWrEn19raN3owGNvTjeQNO0o6STqe4U8Jk4BSKN59VnwcGzLBPBBFxU0QcT3H5vB74Xvp0yaQoOuZuoUgWUAw2fq9ONfOBmemTLHtRvNi/pMFtNPpQb38toxjEpVEMDfah3u08+rRvzYKSNFXSFaXt1av3Nb20U59vP5I+ffJGYGXqJhohaQzFeMP7JO2cPuHyvrSsVnmbtbGckD49dCiwvtQ10iiWz0v6s17qLWs1xlr7UHSV9MsAt1NDkm6WNCG127OSDk2v1wmtPL+mrl2BpyLilb48rwqSrgLupvhAxAkR8e6IuCIiNgzCeWDgtHuwpR0Pit9K2CNN701xgloOXA+MTsuPBeaWnnMWxcDQMkqfcqD4RMmDaV35EyuN6j2Yoq/wBYp3DEv6Ef8/U3R19RbDXODYND0mxbE8xbX3FuzbJ9I+bAQeA76alh9Hz8HGRvUuAMb30k7N4l1JcUuS51Mc3Z9m6gS+Uyr3NeCINH1Kqms5cHKpzFeBzjS9K3Az8BDwY4ouOCgG/S5O+/Lr7vJp3c+ALop31quBI9PyG9k02N2o3s7utuslxi+muv+Q/p5TWnc3sOsW/j8MVDu9McX3LEV302pgLMUbzkeBbUv7fX9qz4vYdIeDM4AzmtVVOs7Ob/d5pHSeGNlkfavnl7rH9GA9fIuJIShdjl8REe9tdyxlkr4EXBkR97Vp+xdQXJHdnOYPAv42Iv66DbEsjIi6350YwG0cCHxqS/ev6naStD9wSkR8aoDq+y7Fx1cfHIj6zPcaGrIkfRD4YUQ82+5YthaSPhoRl9UsOwX4ZhSDesOKpPcCD0XxiZ8trWtItFN3N2VEXNFrYWuZE4GZWeaG/WCxmZk150RgZpY5JwIzs8w5EZiZZc6JwMwsc/8fASaSOGQO1l0AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling:   0%|                                                             | 0/300 [00:00<?, ?it/s]c:\\Users\\jingmingrui\\Anaconda3\\envs\\pd_dep\\lib\\site-packages\\paddle\\fluid\\framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  elif dtype == np.bool:\n",
      "c:\\Users\\jingmingrui\\Anaconda3\\envs\\pd_dep\\lib\\site-packages\\paddle\\tensor\\creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if data.dtype == np.object:\n",
      "Sampling: 100%|###################################################| 300/300 [00:13<00:00, 21.70it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean of max gradient\n",
      "0.1499572\n",
      "Variance of max gradient\n",
      "0.0031638918\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Hyper parameter settings\n",
    "selected_qubit = [2, 4, 6, 8]\n",
    "means, variances = [], []\n",
    "\n",
    "# Keep increasing the number of qubits\n",
    "for N in selected_qubit:\n",
    "    grad_info = []\n",
    "    THETA_SIZE = N                \n",
    "    target = np.random.choice(3, N)\n",
    "    # Generate a value from 0 to 2PI\n",
    "    theta = paddle.rand([THETA_SIZE]).astype('float32') * 2 * pi\n",
    "    theta.stop_gradient = False\n",
    "    cir = rand_circuit(theta, target, N)\n",
    "    \n",
    "    H_l = Hamiltonian(random_pauli_str_generator(N, terms=10))\n",
    "    \n",
    "    grad_mean_list, grad_variance_list = random_sample(cir, loss_func, samples, H_l, mode='max')        \n",
    "    # Record sampling information\n",
    "    means.append(grad_mean_list)\n",
    "    variances.append(grad_variance_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To compare the mean and variance of the maximum gradient of each parameter, we plot them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We then draw the statistical results of this sampled gradient:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "means = np.array(means)\n",
    "variances = np.array(variances)\n",
    "\n",
    "n = np.array(selected_qubit)\n",
    "print(\"We then draw the statistical results of this sampled gradient:\")\n",
    "fig = plt.figure(figsize=plt.figaspect(0.3))\n",
    "\n",
    "# ============= The first figure =============\n",
    "# Calculate the relationship between the average gradient of random sampling and the number of qubits\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.plot(n, means, \"o-.\")\n",
    "plt.xlabel(r\"Qubit #\")\n",
    "plt.ylabel(r\"$ \\partial \\theta_{i} \\langle 0|H |0\\rangle$ Mean\")\n",
    "plt.title(\"Mean of {} sampled gradient\".format(samples))\n",
    "plt.xlim([1,9])\n",
    "plt.grid()\n",
    "\n",
    "# ============= The second figure =============\n",
    "# Calculate the relationship between the variance of the randomly sampled gradient and the number of qubits\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.plot(n, np.log(variances), \"v-\")\n",
    "plt.xlabel(r\"Qubit #\")\n",
    "plt.ylabel(r\"$ \\partial \\theta_{i} \\langle 0|H |0\\rangle$ Variance\")\n",
    "plt.title(\"Variance of {} sampled gradient\".format(samples))\n",
    "plt.xlim([1,9])\n",
    "plt.grid()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It can be seen that as the number of qubits increases, the maximum value of the gradient of all parameters obtained by multiple sampling is constantly close to 0, and the variance is also decreasing."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To further see how the gradient changes as the number of quantum bits increases, we might as well visualize the influence of choosing different qubits on the optimization landscape:\n",
    "\n",
    "![BP-fig-qubit_landscape_compare](./figures/BP-fig-qubit_landscape_compare.png \"(a) Optimization landscape sampled for 2,4,and 6 qubits from left to right in different z-axis scale. (b) Same landscape in a fixed z-axis scale.\")\n",
    "\n",
    "$\\theta_1$ and $\\theta_2$ are the first two circuit parameters, and the remaining parameters are all fixed to $\\pi$. This way, it helps us visualize the shape of this high-dimensional manifold. Unsurprisingly, the landscape becomes more flatter as $n$ increases. **Notice the rapidly decreasing scale in the $z$-axis**. Compared with the 2-qubit case, the optimized landscape of 6 qubits is very flat.\n",
    "\n",
    "Note that only when the network structure and loss function meet certain conditions, i.e. unitary 2-design (see paper [1]), this effect will appear.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Application II: Quantum encoded classical data\n",
    "\n",
    "Supervised learning is one of the important applications of quantum neural networks. However, the barren plateau phenomenon limits the performance of quantum variational algorithms in such problems. Therefore, how to design more efficient circuits and loss functions to avoid the barren plateau phenomenon is one of the important research directions of quantum neural networks at present.\n",
    "\n",
    "In fact, it has been shown that using Renyi divergence as a loss function in the training of generative model can effectively avoid the barren plateau phenomenon [[3]](https://arxiv.org/abs/2106.09567). \n",
    "The gradient analysis tools allow us to quickly analyze the information related to the gradient in a supervised learning model, which can facilitate researchers to try to explore different quantum circuits and loss functions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we present an example using the dataset provided by [Encoding Classical Data into Quantum States](./tutorial/machine_learning/DataEncoding_EN.ipynb)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Paddle Quantum Implement\n",
    "\n",
    "Firstly, import the packages needed for the problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "from paddle_quantum.dataset import Iris\n",
    "from paddle_quantum.gradtool import random_sample_supervised, plot_supervised_loss_grad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Define Quantum Circuits\n",
    "\n",
    "Next, construct the parameterized quantum circuit $U(\\theta)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def U_theta(n: int, depth: int):\n",
    "    # Initialize the quantum circuit\n",
    "    cir = Circuit(n)\n",
    "\n",
    "    # rotation gates \n",
    "    cir.rz()\n",
    "    cir.ry()\n",
    "    cir.rz()\n",
    "\n",
    "    # default depth = 1\n",
    "    # Build adjacent CNOT gates and RY rotation gates \n",
    "    for _ in range(3, depth + 3):\n",
    "        cir.cnot()\n",
    "        cir.ry()\n",
    "        \n",
    "    return cir"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Define Objective Function\n",
    "\n",
    "Here the objective function ``loss_fun`` is defined, and the second parameter is still the variable ``*args``."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss_func(cir: Circuit, *args):\n",
    "    # input the quantum states and training labels\n",
    "    state_in = args[0]\n",
    "    label = args[1]\n",
    "    # Convert Numpy array to tensor\n",
    "    label_pp = paddle.to_tensor(label).reshape([-1, 1])\n",
    "    \n",
    "    Utheta = cir.unitary_matrix()\n",
    "    \n",
    "    # Since Utheta is learned, we use row vector operations here to speed up the training without affecting the results\n",
    "    state_out = state_in @ Utheta\n",
    "    \n",
    "    # Measure the expected value of the Pauli Z operator <Z>\n",
    "    Ob = paddle.to_tensor(pauli_str_to_matrix([[1.0, 'z0']], qubit_num))\n",
    "    E_Z = state_out @ Ob @ paddle.transpose(paddle.conj(state_out), perm=[0, 2, 1])\n",
    "\n",
    "    # Mapping <Z> into label \n",
    "    state_predict = paddle.real(E_Z)[:, 0] * 0.5 + 0.5\n",
    "    loss = paddle.mean((state_predict - label_pp) ** 2) # mean-squared error\n",
    "    \n",
    "    return loss\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Define the dataset\n",
    "\n",
    "Here, we use [Iris dataset](./tutorial/machine_learning/DataEncoding_EN.ipynb) to do the experiment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--Rz(0.275)----Ry(1.589)----Rz(5.910)----*----x----Ry(0.235)--\n",
      "                                         |    |               \n",
      "--Rz(2.328)----Ry(2.518)----Rz(5.586)----x----*----Ry(2.902)--\n",
      "                                                              \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\jingmingrui\\Anaconda3\\envs\\pd_dep\\lib\\site-packages\\paddle\\fluid\\framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  elif dtype == np.bool:\n"
     ]
    }
   ],
   "source": [
    "time_start = time.time()\n",
    "\n",
    "# Hyper parameter settings\n",
    "test_rate = 0.2\n",
    "qubit_num = 2 # Don't give too many qubits, otherwise it will be seriously overfitted\n",
    "depth = 1\n",
    "lr = 0.1\n",
    "BATCH = 4\n",
    "EPOCH = 4\n",
    "SAMPLE = 300\n",
    "\n",
    "# dataset\n",
    "iris = Iris(encoding='amplitude_encoding', num_qubits=qubit_num, test_rate=test_rate, classes=[0,1], return_state=True)\n",
    "\n",
    "# Get inputs and labels for the dataset\n",
    "train_x, train_y = iris.train_x, iris.train_y  # train_x, test_x here is paddle.tensor type,  train_y，test_y here is ndarray type.\n",
    "test_x, test_y = iris.test_x, iris.test_y\n",
    "testing_data_num = len(test_y)\n",
    "training_data_num = len(train_y)\n",
    "\n",
    "\n",
    "# Creating trainable parameters for circuits\n",
    "# Creating Circuits\n",
    "circuit = U_theta(qubit_num, depth)\n",
    "\n",
    "print(circuit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the variation of the loss function values and gradients during training with EPOCH=4 and BATCH=4."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\jingmingrui\\Anaconda3\\envs\\pd_dep\\lib\\site-packages\\paddle\\tensor\\creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if data.dtype == np.object:\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "loss,grad = plot_supervised_loss_grad(circuit, loss_func, N=qubit_num, EPOCH = EPOCH, LR = lr,BATCH = BATCH, TRAIN_X=train_x, TRAIN_Y=train_y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that after ten steps of iteration, the value of the loss function only fluctuates in a small range, indicating that the training process is stable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we randomly sample the initial parameters of the model 300 times, and here we choose the ``max`` mode to see the mean and variance of the maximum gradient for all parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: 100%|###################################################| 300/300 [00:03<00:00, 92.32it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean of max gradient\n",
      "0.15071002\n",
      "Variance of max gradient\n",
      "0.0035270636\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean, variance = random_sample_supervised(circuit,loss_func, N=qubit_num, sample_num=SAMPLE, BATCH=BATCH, TRAIN_X=train_x, TRAIN_Y=train_y, mode='max')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "The trainability problem is a core direction of current research in quantum neural networks, and the gradient analysis tool provided by Quantum Paddle supports users to diagnose the trainability of the model, facilitating the study of subsequent problems such as barren plateaus."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_______\n",
    "\n",
    "## References\n",
    "\n",
    "[1] McClean, J. R., Boixo, S., Smelyanskiy, V. N., Babbush, R. & Neven, H. Barren plateaus in quantum neural network training landscapes. [Nat. Commun. 9, 4812 (2018).](https://www.nature.com/articles/s41467-018-07090-4)\n",
    "\n",
    "[2] Cerezo, M., Sone, A., Volkoff, T., Cincio, L. & Coles, P. J. Cost-Function-Dependent Barren Plateaus in Shallow Quantum Neural Networks. [arXiv:2001.00550 (2020).](https://arxiv.org/abs/2001.00550)\n",
    "\n",
    "[3] Kieferova, Maria, Ortiz Marrero Carlos, and Nathan Wiebe. \"Quantum Generative Training Using R\\'enyi Divergences.\" arXiv preprint [arXiv:2106.09567 (2021).](https://arxiv.org/abs/2106.09567)"
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