research/SingleQubitClassifier.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Single-qubit classifier with data re-uploading tutorial\n",
    "\n",
    "This tutorial shows:\n",
    "- How to construct a fidelity cost function for an optimization problem\n",
    "- How to construct a quantum classifier with one qubit\n",
    "\n",
    "Based on [Data re-uploading for a universal quantum classifier](https://quantum-journal.org/papers/q-2020-02-06-226/), A. Pérez-Salinas, A. Cervera-Lierta, E. Gil-Fuster, and J. I. Latorre, *Quantum **4**, 226 (2020)*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tequila as tq\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy import random\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "Single-qubit operations are just rotations on the Bloch sphere. A collection of single-qubit rotations can be reduced to a single one by combining their angles: you can always move from one point to another on the Bloch sphere with a single operation. \n",
    "\n",
    "Because of this property, a single-qubit classifier with simple parameterized rotations can not treat complex data. Even if it succeeds to classify one data point, it will probably misclassify the others since rotational angles have been only adapted to one particular point. To circumvent this limitation one can introduce the data points into these angles, so each rotation will be data point-dependent. This methodology is called data re-uploading and it can be shown that a single-qubit classifier can be universal using this technique.\n",
    "\n",
    "The strategy to train this single-qubit classifier is the following. Given a problem with 𝑛n classes, we choose 𝑛n vectors on the Bloch sphere. Then, we train the classifier by constructing a cost function that adds penalties if the final state of the classifier is far from the target state that corresponds to its class.\n",
    "\n",
    "The single-qubit classifier circuit is divided into layers. Each layer comprises single-qubit rotations that encode a data training point and parameters to be optimized. $$ L\\left(\\vec{x};\\vec{\\theta}_{i}\\right) = U\\left(\\vec{x}\\right)U\\left(\\vec{\\theta}_{i}\\right) $$\n",
    "By considering more layers, the final state of the classifier will have a richer structure in terms of the data point $\\vec{x}$.\n",
    "\n",
    "$$ \\mathcal{U}_{class}\\left(\\vec{x};\\vec{\\theta}_{1},\\vec{\\theta}_{2},...,\\vec{\\theta}_{l}\\right) = L\\left(\\vec{x};\\vec{\\theta}_{1}\\right)L\\left(\\vec{x};\\vec{\\theta}_{2}\\right)\\cdots L\\left(\\vec{x};\\vec{\\theta}_{l}\\right)$$\n",
    "\n",
    "We will run a $\\mathcal{U}_{class}$ for each training point $\\vec{x}$, but the parameters $\\vec{\\theta}$ are the same. These are the variables to be optimized classically through the cost function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's define the model that we would like to classify. Let's start with a simple model with two classes: a circle of radius $r =\\sqrt{2/\\pi}$ centered at (0,0). Data points will be distributed in a square of length 2 centered at (0,0). The particular choice of the circle radius implies that a random classification will have a $\\sim 50$% accuracy.\n",
    "\n",
    "`circle` function will have two parts:\n",
    "- `random = True`: generate and label random points according to their position inside or outside the circle (used for training)\n",
    "- `random = False`: computes the label of a given point `x_input` (used for testing)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "\n",
    "def circle(samples = False, random = True, x_input = False, center=[0.0, 0.0], radius=np.sqrt(2 / np.pi)):   \n",
    "    \"\"\"\n",
    "    Args:\n",
    "        samples (int): number of samples to generate\n",
    "        random = True: generates and labels sample random points\n",
    "        random = False: labels x_input point\n",
    "        x_input (array[tuple]): given point to be labeled if random = False\n",
    "        center (tuple): center of the circle\n",
    "        radius (float): radius of the circle\n",
    "\n",
    "    Returns:\n",
    "        if random = True:\n",
    "            xvals (array[tuple]): data points coordinates \n",
    "            yvals (array[int]): corresponding data labels\n",
    "        if random = False:\n",
    "            y (int): label of x_input point\n",
    "    \"\"\"\n",
    "    xvals, yvals = [], []\n",
    "\n",
    "    if random == True:\n",
    "        for i in range(samples):\n",
    "            x = 2 * (np.random.rand(2)) - 1\n",
    "            y = 0\n",
    "            if np.linalg.norm(x - center) < radius:\n",
    "                y = 1\n",
    "            xvals.append(x)\n",
    "            yvals.append(y)        \n",
    "        return np.array(xvals), np.array(yvals)\n",
    "    \n",
    "    if random == False:\n",
    "        y = 0\n",
    "        if np.linalg.norm(x_input - center) < radius:\n",
    "            y = 1\n",
    "        return y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Target states\n",
    "\n",
    "Next step is to fix the classes states. The classifier will be trained to return these states depending on the data point. To reduce the uncertanty, target states should be as much distanced as possible. With a single qubit, that means to choose points in the Bloch sphere as much separated as possible.\n",
    "For a two-class problem, an easy choice is $|0\\rangle$ and $|1\\rangle$ states."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# |0> : points inside the circle\n",
    "# |1> : points outside the circle\n",
    "def targ_wfn(y, nclass):\n",
    "    \"\"\"\n",
    "    Arg:\n",
    "        - y (int): class label\n",
    "        - nclass: number of classes\n",
    "    Returns:\n",
    "        - wfn: wavefunction of the target state\n",
    "    \"\"\"\n",
    "    if nclass == 2:\n",
    "        if y==0:\n",
    "            wfn = tq.QubitWaveFunction.from_array(np.asarray([1,0]))\n",
    "        if y==1:\n",
    "            wfn = tq.QubitWaveFunction.from_array(np.asarray([0,1]))\n",
    "    else:\n",
    "        raise Exception(\"nclass = {} is not considered\".format(nclass))\n",
    "    return wfn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Single-qubit classifier circuit\n",
    "\n",
    "The single-qubit classifier has a layer structure, i.e. we have to decide how to design one layer and then how many layers we would like to consider. \n",
    "We will consider the following structure: each layer is a collection of rotational gates which angles are a linear function of a data point with the free parameters to be optimized. In particular,\n",
    "$$L\\left(\\vec{x};\\vec{\\theta}_{i}\\right) = R_{z}\\left(x^{2}+\\theta_{i}^{2}\\right) R_{y}\\left(x^{1}+\\theta_{i}^{1}\\right).$$\n",
    "Then, each layer adds 2 parameters to be optimized. The data points $(x^1,x^2)$ are re-uploaded in each layer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# single-qubit quantum classifier circuit\n",
    "def qcircuit(xval, param):\n",
    "    \"\"\"\n",
    "    Arg:\n",
    "        - xval (array[tuple]): data point\n",
    "        - param (dict): parameters dictionary\n",
    "    Returns:\n",
    "        - qc: quantum circuit\n",
    "    \"\"\"\n",
    "    layers = int((len(param))/2) # 2 parameters/layer\n",
    "    # initialize the circuit \n",
    "    qc = tq.gates.Rz(0.0,0)\n",
    "    for p in range(0,2*layers-1):\n",
    "        # add layers to the circuit\n",
    "        qc += tq.gates.Ry(xval[0] + param[p],0) + tq.gates.Rz(xval[1] + param[p+1],0) \n",
    "    return qc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cost function\n",
    "\n",
    "The cost function for this quantum classifier model will be constructed from the fidelity of the classifier final state respect to the target state of its corresponding class. It will penalize that the output state is far from its label state.\n",
    "\n",
    "First, we define the fidelity between two states as an objective (see State Preparation Tutorial). Then, we construct the simplest cost function of this kind: average of squared infidelities for all training points $M$: $$ \\chi^2 = \\sum_{i=1}^{M}\\left(1-|\\langle\\psi_{target}|\\psi_{circuit}\\rangle|^2\\right)^2$$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Fidelity objective\n",
    "def fid(wfn_targ, qc):\n",
    "    \"\"\"\n",
    "    Arg:\n",
    "        - wfn_targ: target wavefunction\n",
    "        - qc : quantum circuit \n",
    "    Returns:\n",
    "        - O: objective\n",
    "    \"\"\"  \n",
    "    rho_targ =  tq.paulis.Projector(wfn=wfn_targ)\n",
    "    O = tq.Objective.ExpectationValue(U=qc, H=rho_targ)\n",
    "    # fidelity = tq.simulate(O)\n",
    "    return O \n",
    "\n",
    "# cost function: sum of all infidelities for each data point respect the label state\n",
    "def cost(x, y, param, nclass):\n",
    "    \"\"\"\n",
    "    Arg:\n",
    "        - x (array[tuple]): training points\n",
    "        - y (array[int]): labels of training points\n",
    "        - param (dict): parameters dictionary\n",
    "        - nclass (int): number of classes\n",
    "    Returns:\n",
    "        - loss/ len(x): loss objective\n",
    "    \"\"\"  \n",
    "    loss = 0.0\n",
    "    # M = len(y): number of training points\n",
    "    for i in range(len(y)):\n",
    "        \n",
    "        # state generated by the classifier\n",
    "        qc = qcircuit(x[i], param)\n",
    "        # fidelity objective respect to the label state\n",
    "        f = fid(targ_wfn(y[i],nclass), qc)\n",
    "        \n",
    "        loss = loss + (1 - f)**2\n",
    "        \n",
    "    return loss / len(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training\n",
    "\n",
    "We have now all the ingredients to train a single-qubit classifier with data re-uploading.  \n",
    "If a gradient based optimization is chosen for this type of optimization problems, numerical gradients are adviced since analytical ones become quite expensive."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimizer: <class 'tequila.optimizers.optimizer_gd.OptimizerGD'> \n",
      "backend         : qulacs\n",
      "samples         : None\n",
      "save_history    : True\n",
      "noise           : None\n",
      "\n",
      "Objective       : 400 expectationvalues\n",
      "Gradient        : 2400 expectationvalues\n",
      "gradient instr  : {'method': '2-point', 'stepsize': 0.0001}\n",
      "active variables : 6\n",
      "Iteration: 1 , Energy: +0.23346574, angles: {th_3: 4.946478475226956, th_1: -1.984857687022879, th_5: 6.094228093092652, th_0: -1.7808298315353657, th_2: 2.0305330159430013, th_4: 8.89720462977007}\n",
      "Iteration: 2 , Energy: +0.24568509, angles: {th_3: 5.177458750101836, th_1: -1.5046410048962369, th_5: 6.094228093092652, th_0: -1.9668793788050198, th_2: 0.25366461000251084, th_4: 9.429982384992186}\n",
      "Iteration: 3 , Energy: +0.34273167, angles: {th_3: 2.610709683911139, th_1: -4.11965271230925, th_5: 6.094228093092652, th_0: -3.990162105280362, th_2: -0.837018339540754, th_4: 12.077363592549728}\n",
      "Iteration: 4 , Energy: +0.41100568, angles: {th_3: 4.081797701231221, th_1: -4.1998105692556384, th_5: 6.094228092741568, th_0: -2.9373123644616017, th_2: -1.5325493513295756, th_4: 13.399512918875173}\n",
      "Iteration: 5 , Energy: +0.31916175, angles: {th_3: 2.391303024200917, th_1: -6.472994601839014, th_5: 6.094228092566027, th_0: -1.469593533147448, th_2: -2.518924236681155, th_4: 16.237487146769446}\n",
      "Iteration: 6 , Energy: +0.18903087, angles: {th_3: 0.6054755106135814, th_1: -4.350076845031609, th_5: 6.094228092566027, th_0: -1.1529563858416918, th_2: -0.7674481295413216, th_4: 18.32308007272708}\n",
      "Iteration: 7 , Energy: +0.24706587, angles: {th_3: 1.4170489917460554, th_1: -4.558366452437925, th_5: 6.094228092653798, th_0: -2.1858732633280455, th_2: -0.9235025623782028, th_4: 18.780993200577786}\n",
      "Iteration: 8 , Energy: +0.18957480, angles: {th_3: 1.9605822789058145, th_1: -5.527640916329952, th_5: 6.094228092917111, th_0: -0.6687996002617134, th_2: -0.6889772782590158, th_4: 18.081389154242707}\n",
      "Iteration: 9 , Energy: +0.28645830, angles: {th_3: 1.5788772007046856, th_1: -5.638779777627052, th_5: 6.094228092917111, th_0: -1.4139949979544377, th_2: -1.1512637374432393, th_4: 18.302153905481166}\n",
      "Iteration: 10 , Energy: +0.27527401, angles: {th_3: 1.9429922146972913, th_1: -3.3228180477941693, th_5: 6.094228092917111, th_0: -0.24408389064543945, th_2: -0.4065263357136326, th_4: 18.028189277072833}\n",
      "Iteration: 11 , Energy: +0.35620661, angles: {th_3: 1.0124985821386665, th_1: -2.7198954044125903, th_5: 6.094228092917111, th_0: -1.1758665832184727, th_2: 0.5522929556759827, th_4: 18.22237564643069}\n",
      "Iteration: 12 , Energy: +0.44487047, angles: {th_3: 1.1112520918477444, th_1: -3.9067179067828812, th_5: 6.094228092566027, th_0: -0.18357759524889428, th_2: 0.03411429510428532, th_4: 16.46264976481032}\n",
      "Iteration: 13 , Energy: +0.42685449, angles: {th_3: 1.2325104045554103, th_1: -4.072692525957542, th_5: 6.094228092566027, th_0: 0.10939902088916315, th_2: -0.055096351638694016, th_4: 16.59816347483484}\n",
      "Iteration: 14 , Energy: +0.34285833, angles: {th_3: 1.4761533353437757, th_1: -4.352859605727501, th_5: 6.094228092390486, th_0: 0.5966751190598111, th_2: -0.15525908773195382, th_4: 15.946300817175157}\n",
      "Iteration: 15 , Energy: +0.24247172, angles: {th_3: 1.6173198552966495, th_1: -4.1330938378716136, th_5: 6.094228092390486, th_0: 1.65366489806398, th_2: -0.6388307499464642, th_4: 16.87896707644589}\n",
      "Iteration: 16 , Energy: +0.39483818, angles: {th_3: 2.8481206217076585, th_1: -4.487703249247993, th_5: 6.094228092390486, th_0: 1.8400279979008418, th_2: -0.9650933280230857, th_4: 15.585817651249961}\n",
      "Iteration: 17 , Energy: +0.27508621, angles: {th_3: 2.2162219128518137, th_1: -5.889468130975258, th_5: 6.094228092214944, th_0: 2.937610605260691, th_2: 0.43306029369383003, th_4: 15.90076008635952}\n",
      "Iteration: 18 , Energy: +0.48031298, angles: {th_3: 2.684871117752545, th_1: -6.800326063824976, th_5: 6.094228092214944, th_0: 1.7001186344333665, th_2: -0.34452812545836253, th_4: 15.313179237809887}\n",
      "Iteration: 19 , Energy: +0.21267641, angles: {th_3: 2.286365476919264, th_1: -6.659406894086995, th_5: 6.094228092214944, th_0: 2.0929719729582534, th_2: 0.3059640782082854, th_4: 16.222552166459543}\n",
      "Iteration: 20 , Energy: +0.32503084, angles: {th_3: 3.2241173588294663, th_1: -5.657084658027705, th_5: 6.094228092214944, th_0: 2.6679421963461443, th_2: 1.6407345543803808, th_4: 15.467050145055921}\n",
      "Iteration: 21 , Energy: +0.27935990, angles: {th_3: 4.221413997884369, th_1: -6.374904874373444, th_5: 6.094228092214944, th_0: 2.612994029050794, th_2: 0.6782232406793727, th_4: 14.86419372549831}\n",
      "Iteration: 22 , Energy: +0.19863393, angles: {th_3: 3.47027118879744, th_1: -6.338229376646779, th_5: 6.094228092214944, th_0: 1.9971066773120791, th_2: 1.194983782417867, th_4: 15.27353515841565}\n",
      "Iteration: 23 , Energy: +0.26671554, angles: {th_3: 3.662205090196048, th_1: -5.707411470049467, th_5: 6.094228092039403, th_0: 2.8099838552259264, th_2: 1.389251309702725, th_4: 14.850343188441416}\n",
      "Iteration: 24 , Energy: +0.21274836, angles: {th_3: 3.0898423342680106, th_1: -6.5519832630022545, th_5: 6.094228092214944, th_0: 2.152020370382946, th_2: 0.9887132300617262, th_4: 15.296486874185222}\n",
      "Iteration: 25 , Energy: +0.36602784, angles: {th_3: 2.6891695311404993, th_1: -5.936112863610033, th_5: 6.094228092127174, th_0: 2.980234658898297, th_2: 1.5815527807912622, th_4: 15.560262926035247}\n",
      "Iteration: 26 , Energy: +0.24158921, angles: {th_3: 3.409715353455571, th_1: -6.361890418817886, th_5: 6.094228092127174, th_0: 3.022455564057973, th_2: 0.6262280088869862, th_4: 14.50904115792866}\n",
      "Iteration: 27 , Energy: +0.18608619, angles: {th_3: 3.0834232299395294, th_1: -6.296330472820181, th_5: 6.094228092039403, th_0: 2.7872761259614878, th_2: 1.023418502075567, th_4: 14.952048996853069}\n",
      "Iteration: 28 , Energy: +0.17754118, angles: {th_3: 3.0371505017716784, th_1: -6.492048609689606, th_5: 6.094228092039403, th_0: 2.2877832968744105, th_2: 1.2395874129421671, th_4: 15.086758626511878}\n",
      "Iteration: 29 , Energy: +0.18608412, angles: {th_3: 3.074299424409819, th_1: -6.204269435559897, th_5: 6.094228091863862, th_0: 2.75714679055503, th_2: 1.3003205205787245, th_4: 14.780658253368301}\n",
      "Iteration: 30 , Energy: +0.21493439, angles: {th_3: 3.1577509559180865, th_1: -6.639392298741426, th_5: 6.094228092039403, th_0: 1.9995711417799913, th_2: 1.1828672166361436, th_4: 14.663838792706517}\n",
      "Iteration: 31 , Energy: +0.34254717, angles: {th_3: 3.2213886056114784, th_1: -5.7084740834087855, th_5: 6.094228092127174, th_0: 2.709958474367021, th_2: 2.166789939531257, th_4: 14.281913449927501}\n",
      "Iteration: 32 , Energy: +0.16377244, angles: {th_3: 2.8757783340131784, th_1: -6.742959592116579, th_5: 6.094228092127174, th_0: 2.326440389557296, th_2: 1.528269897793077, th_4: 14.203612756148074}\n",
      "Iteration: 33 , Energy: +0.20947398, angles: {th_3: 3.239703089715265, th_1: -6.349045734168509, th_5: 6.094228092127174, th_0: 2.4778918825144505, th_2: 2.137200149949036, th_4: 14.531946217524446}\n",
      "Iteration: 34 , Energy: +0.22543889, angles: {th_3: 3.4614157573555455, th_1: -7.034369045003935, th_5: 6.094228092214944, th_0: 2.067083095824484, th_2: 1.2204399760451303, th_4: 13.693325353763923}\n",
      "Iteration: 35 , Energy: +0.21571020, angles: {th_3: 3.790969245517053, th_1: -6.904596024140315, th_5: 6.094228092127174, th_0: 1.9319416376325338, th_2: 1.2330038975521695, th_4: 14.0769633595208}\n",
      "Iteration: 36 , Energy: +0.19462980, angles: {th_3: 3.5106090007235586, th_1: -6.648830769599903, th_5: 6.094228092127174, th_0: 1.9596364079983677, th_2: 1.2136058321458942, th_4: 13.967210009026068}\n",
      "Iteration: 37 , Energy: +0.15196217, angles: {th_3: 3.2645398521838014, th_1: -6.523197874516416, th_5: 6.094228092302715, th_0: 1.8983517410764497, th_2: 1.4826854004867693, th_4: 14.406907729572346}\n",
      "Iteration: 38 , Energy: +0.20612016, angles: {th_3: 3.281643959582436, th_1: -6.042624303725983, th_5: 6.094228092390486, th_0: 2.286633100883763, th_2: 1.8936310652527946, th_4: 14.07461250620441}\n",
      "Iteration: 39 , Energy: +0.25849102, angles: {th_3: 2.5626097961751575, th_1: -6.9244844223056825, th_5: 6.094228092390486, th_0: 1.5694612639252516, th_2: 1.7455295850302581, th_4: 14.472298554297666}\n",
      "Iteration: 40 , Energy: +0.27171714, angles: {th_3: 2.8985899398239416, th_1: -7.066848416023331, th_5: 6.094228092214944, th_0: 2.3009155169940034, th_2: 2.3215461628340415, th_4: 14.900547121215178}\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 41 , Energy: +0.27351703, angles: {th_3: 3.452908352358718, th_1: -7.398473506404077, th_5: 6.094228092214944, th_0: 1.627776254006628, th_2: 1.2608637559952656, th_4: 13.63493103602002}\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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     ]
    }
   ],
   "source": [
    "layers = 3\n",
    "nclass = 2\n",
    "training_set = 400\n",
    "\n",
    "# generate the training set and its corresponding labels\n",
    "xdata, ydata = circle(training_set)\n",
    "\n",
    "# generate the variational parameters\n",
    "param = [tq.Variable(name='th_{}'.format(i)) for i in range(0,2*layers)]\n",
    "\n",
    "# initialize the variational parameters\n",
    "# note that due to the random initialization the result can be different from time to time\n",
    "# With gradient based optimization you might get stuck\n",
    "inval = {key : random.uniform(0, 2*np.pi) for key in param}\n",
    "\n",
    "grad = '2-point' # numerical gradient (= None: analytical gradient)\n",
    "mthd = 'rmsprop' # scipy minimization method\n",
    "mthd_opt = {'eps':1.e-4} # method options (that's the stepsize for the gradients)\n",
    "\n",
    "obj = cost(xdata, ydata, param, nclass) # objective to be optimized: cost function\n",
    "\n",
    "t0 = time.time()\n",
    "# depending on the optimizer this will take a while\n",
    "test = tq.minimize(objective=obj, initial_values=inval, method = mthd,\n",
    "                                   gradient = grad, method_options = mthd_opt, silent=False)\n",
    "t1 = time.time()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extract the results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss =  0.11884156841701687\n",
      "method:  rmsprop\n",
      "method parameters:  {'eps': 0.0001}\n",
      "execution time =  35.648783659935  min\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": [
      "None\n"
     ]
    },
    {
     "data": {
      "image/png": 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VzJ49m+9///vs22eYWt+vhL3tR9ey+J4HkhbDGfNO4pTFVwW8c6VwFBVjianwaMtzMGfB6Sil8Lp754mHsm1CN5Ev/vVOeJtMDhIEY7LWI0/kQY8uHE1te21ce2VhIIlmuHM4vznu17Q1NQbqgFssuFr392qxZaN65Gb84Ac/4MYbb0QpxY033si1117L/fffn/a5B5rYGLzRQObbj/6x58WoI3AUFUcV/gLjbBtvcIwjxEBVcOwx/72X7f1xjv6wSRgYUprZmSl6WzQrFCOPDK84rU6WfW0ZZ0w+I26xZQiUkk2lBnlRURFtwWqEsYOdd9xxB21tbSxbtqzHfhINlPblbNb+JpUJS3GzVk3EwLRPpbj20bWm/ScjMpH7OAqLUAo629qi3oeOhfiMHlueg4NPmB+X/27WboayWnEUFPQ6HNUXOIqK8XS68CdYaNzoGKNr2dfvi0eUM/nQI9n+4fsJf6cD9T7WvnRvfmYzO3NSyCFx1opRpUEI1DcZecCkpPofPnw49fX12O32lIW8traWysrA08Fdd93Fe++9x6OPPhq332AS8kRT68PVFlP8AzbrM7JfI4E2i+mHRSYLRVMYeqRTabSvpugPGGdMPsMw3RDMl1Izazci3XrkANdddx0bN25EKcXEiRO59957Uzo+F5l3wSWGXmtIbNN57DbqM4TZLFKjSUch3G0i4EL2kMkwYc565InIhEfeHwwmjxz6ZpGKnmqwQPTjfDq1ZARhwOghTBi/+yDzyBNhttxaKostC6mTruedTJ+JYvDiaQu5SqZqCOVk+mFPGNX+TnWx5WRIpR650DsGY9Eso1TObENZrTiLB2ZVrcFOJmsIZfdfUS9wte7HWVTcpwJwzz339FnfQjSJ4uW9xTDTwmBANNVMlWSyc7It5bC3qYjZkhWSDZkqfZG1YsagjJH7vB4adu6gqGwERcPLMtJnXzDYYuR9TTLx8hChiUVmIpOR2umSWy30M4Mu/TARHS3N7N/bQPn4A7DlZW/5WhHy9OipbIAsIC0MVobEYKerdX/3bE6l8Lg7s1rIhfSIrR2TqqctCIONQSPksbM5tdbsb6gHyPggpzDw9EWGjCDkKjmbtdKydi1VJ89ny4yZVJ08n71PPBFX60NrTVtTY1r9R5ax3bFjB7NmzUr62KamJhYsWMDUqVNZsGBBVhTNEgRh8JKTQt6ydi21N96Et6YGtMZbU0Pb3f+L+/U34vZNZTZnJL2pR75y5Urmz59PVVUV8+fPZ+XKlWn3JQiC0BNZG1rZ+d34/Mrib55G2UUXUf+ru9Cd0fXIcbtx3XsfjpNOxN+yn/Zbg+KpFG6HkwP+ZLyOpBG9rUe+Zs0a3njjDQAuvfRSTjzxRG677bakzy8IgpAKOemRe+vqDNu1Qe6v1Zb6Wp29rUe+Z8+ecNGsyspK6uvrU7ZBEAQhWbLWI0/kQdsqKwNhlRiso0cDYCkZRukdv6SobETGBjpTqUcuCILQn+SkR16x5BqU0xnVppxOyq/5IQAlI0cx8oBJGc1WcTi617y0Wq14E8TeR40aRW1tYOGL2tpaKioqMmaHIAhCLDkp5CVnnUXlzcuxjRkDSmEbM4bKm5dTsOAUAKx5qYdTYrHb7Xg8nrSOPfvss3nooYcAeOihh1i4cGGv7REEQTAja0MrPVFy1lmUnHVWVFt7cyDNz2bv/SSg3tQjv/7661m0aBF/+MMfmDBhAn/96197bY8gCIIZg2qKvtfThaezM2cmAMkUfUEQUmFITNG32fMy4o0LgiDkEoNGyLXWdLa3YXc4sdl7HyNPhiuvvJJ169ZFtV199dVcdtll/XJ+QRAEGERC7vf5aNlTR3H5SGwlpf1yTqlHLghCNpCTWStG+IIZJv3ljQuCIGQLSQu5Uup+pVS9UmpzRFuZUuoVpVRV8HV435jZM15PF5CZjBVBEIRcIhWP/EHgtJi264FXtdZTgVeDnwcEb1cXyqKyfg1EQRCETJO06mmt31JKTYxpXgicGHz/EPAG8JMM2NUjn79XxztrttHW5KaozMEhJw7ngJlFKKX64/SCIAhZQ29j5KO01rUAwVfTuehKqcVKqfVKqfUNDT2vuZiIz9+r4/WHt9LWFFjqq63Jzftr69mzM3Mi3pt65EuXLmX69OnMnj2bc889l+bm5ozZJQiCEEu/xSG01quB1RCYENTT/n+784O4tgMPr+CQE8fxztPb8Hb5o7Z5PX7WPbGNSbNLQDl58d7NUdvPvfawlOy95ZZbuOGGG1I6JsSCBQu49dZbsdls/OQnP+HWW2+VMraCIPQZvfXI9yilKgGCr/1Sr7Vtn/Giu10uP/sb6ulsiy9nmwqR9cgvvvhigHA98oMPPphTTjkFl8tlevwpp5yCLRirP+aYY6iuru6VPYIgCInorUf+DHApsDL4uqbXFgVJ5EEXlTnCYZVI8odZ0Vrjde9P2QOPZOXKlaxatYqNGzcCgdBKVVUVjzzyCPfddx+LFi3iySef5Dvf+U6Pfd1///2cf/75adsiCILQE6mkHz4CvANMU0pVK6X+nYCAL1BKVQELgp/7nGMXTsGWF2261aaYNa8ESH95t0SkU498xYoV2Gy2sFcvCILQF6SStXKhyab5GbIlacbPLODw08rY9MY+XPt95A+zMmteCRNmFgJg7YMUxNh65IlCKxAoX/vss8/y6quvSiaNIAh9Ss4lXbta97O/oZ5x0/IZNy1+zUylFEVlI3p9nlA9cnsaM0VffPFFbrvtNt58800KCgp6bYsgCEIicm6KfltTI2ald602G8NGVmSkjG2oHnk6YZGrrrqK1tZWFixYwNy5c7niiit6bY8gCIIZOVePvG5blem20VOm9tq2/kTqkQuCkApm9chzziM3i3/3RVxcEAQhF8g59SsqG8H+hvqo8Eqm4uKpIvXIBUHIBnJOyEPx75b6PUDAEy8qGzEgy7tJPXJBELKBnBNyALszkK0ybGQFBcNKBtgaQRCEgSXnYuQAPm9gEQmrLCIhCIKQm0KufX4sFgs2mwi5IAhCToZWnEVFbP/wfZ6+439obdxL8Yhy5l1wCTPmnTTQpgmCIPQ7OemRb3n7dV5ZvYrWvQ2gNa17G3h59Sq2vP16xs7Rm3rkIe644w6UUuzduzdjdgmCIMSStR75Y7+IXzVu2jHzmHvqGbz58AN4u6KrH3q73Lz24GpmzDuJjv0trL3r1qjt5/88tXpevalHDrBr1y5eeeUVJkyYkHYfgiAIyZBzHrnWmvZ9TYbbeluHPERv65EDLFmyhF/+8pdSMEsQhD4naz1yMw/a7/NRUDqcjuZ9cduKy0cCUDCsJGUPPJLe1iN/5plnGDt2LHPmzEnbBkEQhGTJOY/c6/Ewd8Hp2PLyotpteQ7mXXBJn5032XrkHR0drFixguXLl/eZLYIgCJHknJD7vB4mHXoE87//g4AHrhTF5SM5ZfFVfZq1EluP3GuyeMW2bdv48ssvmTNnDhMnTqS6uprDDjuMurq6PrNNEIShTdaGVsxQBLzvmSfMZ9ZJC/rsPOnWIz/kkEOor+9eunTixImsX7+e8vLyTJsoCIIA5KBH7iwqpnz8BCyWvjW9N/XIBUEQ+pOcq0c+mBiK31kQhPQZNPXIG6t30WaSfigIgjAUyZkYebO7mfr2eoa5Fa2qg2pdj8/vw6qsoEj43m6xU5RXRFtXGx6/J6ljknm/4icr+PBfH6K1DueLX3z5xXzr4m8l1U9dex3nP3Q+owtHc/y443mr+i3q2usYljcMpRQt7pase5/ttma7fblka7bbl0u2xto3unA0Vx92NWdMPiMj+phVoZXp06cbTqBpdjdT01aDxQelrXbaCry47f7+MrdP0FpTt6OOJZ8uGWhTBEEYAJxWJ8u+tiwlMc/60IrT6aSx0Xhh5fr2euxdimFtgQeIApeVPE/WmJ4yWmu6WrvY5do10KYIgjBAdPo6+fUHv85IX1kTWhk3bhzV1dU0NDTEbatvqcXRZSUyMq4Bd54Pr7X/nyh6i0azy7WL+766b6BNEQRhAKlrz8z8kqwRcrvdzqRJkwy3PXnZj8nviA+5tDm9PHHy7r42TRAEoU8YXTg6I/3kRHzCSMQBCjut/WyJIAhCZnBanVx92NUZ6SsnhDxUDCuWdqePfEsx+ArRGvAVUGAdhkJRkldCqaMUhaKysJLzp51PZWFl3LZseJ/t9uWSrdluXy7Zmu325ZKtsfZVFlamPNCZiKwJrSTiwCMX8uELDwKR9U1sjDnkAlo/L8fl8YVbvXYrt553COccOra/zRRyiKc/3M3tL31Ga7OL4tJ8fnzqNM45dKxpuyBkMxkRcqXUDqAV8AFeo/SY3rDr85HYChbg7fwH+FvBUozN+XUato3GVRK9wITL4+P2lz6Tfz7BlKc/3M1Pn/o47ADsbnbx06c+Zv3OJp7csDuuPcTtL31GTbOLMaX5LI0R/t62h+wy2yYIichIHnlQyI/QWie1pplRHnki7rniNcN2jeaO0s54e4AvV2bmkUXIbYzE8faXPmN3c/zCIFal8Jn8PygCmVIh8u1W/u3wsVHCn277recdAhB1c4nd1pc3kXRuLtnWnmu2potZHnlOCPlDN6yjrckd196i/KwuiW8fW5rPuutPTrp/YXAS63lDQBwjP2cDiW4gEH8TCX3u6/bSfDvtXV48Pp30MWKrebvdoihy2mju8KQt7H09IUgDLyulNiilFpsYsFgptV4ptd4oVzwRxy6cgi0v2lQPmrec8TXB8+1Wlp46LaX+hdzg6Q93c9zK15h0/XMct/I1nv4wcerp7S99FifaLo8Pa5atvpdIxCFaDCI/93V7s8sTJYz9ee7BaKvHr9nX4UHTHbbr6W84WTIl5MdprQ8DvglcqZQ6PnYHrfVqrfURWusjRo40zkIx46CjR3PSxdMpKAmsCtShNC/me9jqiP4nHVuaLwOdg5SQd7272ZX0P0KNQfgEwBf7HyYIA0BoPC8TZGSwU2tdE3ytV0r9DTgKeCsTfYc46OjRTJxTzn3XvMVHBT622uNjiYNdwIfyYJiZd200sB26Tj3pdeyjryD0N2bORqr02iNXShUqpYpD74FTgM297deIPKeNsjGFnDJzVLgt5IW3ur1cuPrdvjhtVpCORzqYMPuDj22PvE49oQnEp40ozbeTb4+ecJbpiIzZuYWhw5jS/Iz0k4nQyijgH0qpj4B/Ac9prV/MQL+GXHjT0Zy2KBADX77wYNZdfzLnHDqWdreXd7Y30tLhAVKPp2Y7iTzSoYDZH7yGqN+v0XVKhE/rOMHOt1tZdvbB3HreIYwtzUcRcBjuOn8ud58/13D/7xwzIaX2u8+fy52L5iR9jIp57a92u0UxvMA+IOceTLaW5tuxxwzOZHI8r9ehFa31dmBOBmxJml1NHQCMLysIt02tKALgi4ZWdjW5DPOEgZwNRSTrkQ5Wlp46jeuf2kSnJ7588e5mF0se28g1j21Mud+xESmJRiErs78Xo/2POKAspfZ0+pL0vty0NZFNmSBr6pEny+fv1/HGM9tY2dXMy9eewIFBAf+qsYPjb3+d2/7tEP731S8MH61zOS3xuJWv5dR3yvQfrdaaY299lRaXN630wdJ8O26v3zBPO1dv7sLQI+vrkSeLt8uPp8HN+QdXMm549+P22OH5OGwWqva0DUrvdck3psa1hR7Nsi2M1Bfx/E3VLdTtd3PjmTNTjlWbhUpExIXBQk7UWomkpDwg3v951EScEXFEq0Vx6sGjGVnsYExpvqH3mqmBhYHAbgvcc0cU5tHU3hUYqLMornlsY1T2hVkYqT8yXkLnMLr2Lo+Pax7byO0vfZbSuWP7VEqb/n5jUZB0qEQQcpmcE/JhIwNivL/BBdOjt/3vhYcCMGqYM25Gn9NuyemJQi9/uoeJIwp47doTeeqDapY+sYk2d2BCVGxwLDYtz6y2CGRO2IxmURqRTP2SRH0uX7vFcKp7LNkachKEviDnhLyw1IEPzZp1Ozl4XrwIaa1ZOHcMG3Y28fSHNbS5vYwocnDDN6fnpDcW6UlXDHPwzEc13PX3qh7znyPDSKnkYBudtyTfjlIYTi1O5IWbEfLOe3qSMLP79a0N3HreIeHzGtVBybyvPDwAACAASURBVOWbtiCkSs4JeZfPzza7nynDnHHb3tnWyBV/3sCf/v0otu9tp7LUyctLThgAKzNDrEe6Z787Ka8XutPylp46jZpmFyfu2sD3Pn2Bka5mGvJLeXDmN3mDw5n7i5fDIh0S7H0dnihxbHZ5wv3GetTJ2mNmYySxN5dEYx3nHDpWqgYKQpCcE/LdzS7WFHZx17EVcdtGFjtocXn4qLqF97/cx/eOmwgEBH773jYuPvqAfrbWnJa1a6m/6268tbXYKiupWHINJWedFbWPea2QxEWWQkz9+B8Mf/y/ebZjH9A9sj3K1czVG58A4I3xh4f3jxTsRL27PD6uffyjpGxIlZpmV48zM2PHOiJFXRCGIjkn5F8Fc8gnROSQhzhgRAE2i+JP7+ygy+fnhIMCNV2e/7iWpz6o5vwjxmOzDlyiTkigDvr4H1y98QkcvoBwemtqqL3xJoAoMTevFaKjqvgZedsAV298AqfPY9iH0+fhug2P8L1PXwh45+MPN/baI4Q+1oaeMCvdmoiSfHtCL1/CJoIQT84J+a6mDmZ2Wfnwfzcz6+ZjcQRncgE8t6kWgM/3tKGA2qAQHj25jD+9u5PNNfuZO750IMyOCpOs+PSFsIiH0J2dbFp2K5ess4TDA5UlTg7avC4srq32fFCKYV0deMsreHDGN9nX0RV1Uwh5226r3VTEQ6iI/Wc07uCUXevDx0R67UDSAh9ibGn85Jae4ugOmwWlMBXxsRI2EQRDck7I54wrZd/s0bjfbWL/3k5GTggIeUgovf6Ap6iBG9d8gs1q4WsHjgDgve2NAybkkWGSka5mw33K2vdF5V1/p/1TTo/wqks83UJo31vP4vcfw+J04osRbKfPE3ejSITT5+GMne9ijfGynT4PV2x6GoffayjwRl78Xw45g9OXXBYltqHQh1EWSmQs3q8DZT6NUCBZKIJgQu4J+fhSxpw8hcffbWJ/o4uRE4qBxJkZ6w49mZHFefzqlc9Z+cLWARkQiwyTNOSXMspAzBvyu28yLo+Pr79uHhqBgBfv64xfISkdLCahkmEeV9wEHKfPw48/eJSlGx4JHBtsD4n8uOo5YHBtI7NRIgcmAZY+8VG4nvR0t5XjO20M04r9KlB3vnVUXu+/pCAMUnJOyD+ra6WsKGD2/oZuEUuU4fD0h7tpavfgC3rrA1F7JXISy4MzvxkXv3Zb7OHYdohy1760z9dmdZCnfTj83Ytv+Al4tqnMjDTbN9Z7D2HpclN/191xA7chIgcmW9aupf7aS/DU1HBfMGRTV3EUp3dYsarA7aFEK87osFI2eXQKVgvC0CKnhFxrzXm/Wce3jxjPuAIb+/d2i3ei2Zy3v/RZWMRD9PcizUtPnRb2Ot8YfzilnW2cs/1tKoKx7z8cfEY47hwKVyQjuKqgAN3REdde5HOjgRZ7AcWejnBsu6wgj8XvP4aO8eQNz2W3Yy0sZHfegWybfDZuRxkOdxNTtj/D6PpArZy6iiPit9Wsp+rk+YaZOCFa1q6l9sab0J2dUbH6fxw7F4utKGpfi7LieacGFs1M4ooIwtAjp4S8qb2L9i4fY1p8+P2azW/tZsfmvRy7cApLT51muD7j0lOnscSkKp5RLeu+WkT1nEPH8utXP2dXk4vhbU1c/smz/G72QtZO/nrUfifu2pAw2yQW3dEBSmEpKcHf3B2uCXneDr+H2w+/kDfGHx4uElVZfXAg9bGmxrxjqxX8fnbnHcjWaRfhtzoAcDtHsHXaReHdzLaNrllPzdLrqFl6Haq0FAvga2kJp1rW33V33M3E6fNgsRYamtPeoUxTNpNJ5RSEwUzOVD98+sPdrHhuCyMavZzWaceuu31IW56Fky6ezqd5PkPBTaZyoNlCvYlWPk9FzGtbXPz0P2/nh9v/jnNfAwr47ayzeebA4ynwuJi3exPvj5rOr976P8P4uQYsIUFsjt+unM7AwKfBtj35pfzs/BVxN6AtM2aC2arxDgfa7WbdMctxO0fEbXd0NgKYbjvu3ZtMrkQ3Rt78tslnm/b59Y23RIm/cjopOfccWv72dFx75c3LReSFQYdZ9cOcEPJIkV3c4qBEx+eCF5U5uPSW43o8PkSsGJuJvdnkm2RreYSExFNTExDjiG2dVju/nvstqoZP4Pd/v432vHwKuqIHFyPFrmiEk2MXTkH99OLE3nQsSjFjy6dxzVUnzzfux2oFX+BavXbCKjBaySZ0TUy2nfzmVQlNqqs4Isqbj+ozpl+Lz830qkcZXfevhH1GYhszhool14TDN+FuI0ReEHKNnC5jG5mRMkwbR47bmtymx59z6FhuPe8QSvIDqYqjhjniPOpEk2+MSKYkbsvatVT/7Ea8NTUo4i+20+fhe5++wNR9X+FHUWgg4lunXRTwUJWircnN6w9vpdqb3JNAXcURrDtmOa8d/388dMM6Pn+vLmp7xZJrUM7oUgfK6QyLOIDD3WTSe/wCDz0f0822yWdHizgExDv0o3VY2Cd9+WxKIg7gra01DN/ozk7q77o7pb4EIdvJiRh5ZK2QL+b8yPDRu6jMYXBkN+ccOpYZlcM49e63WHrq9Lg6Hak+lyQqiRvqc8VjtzCqy/wGA4Gc8n/f+iIWAwuMxM7b5Wf71HMYXf9+uC3Sa3d27WPytjVAdPw6dBOAwELW0D2LNDb0EBk/n7L9GbZMvwRtiV56DBXzOYjF52bK9mdMv2+krQlRCkfnPrTFSqGrPvG+BtgqK/HW1hpu89bWmoZcPn+vjnfWbKOtyU1RmYNjF04JXy9ByFZyQsjPbfyY7wYHAPX2Z+IeyW15Fo5dOKXHfqZWFDHMaWP9jia+dfi4pEuvxmI0TTyyCmBokovZxJ9I8saModxEcMzErtNegnI60Z2dcSGKTkcZW6dfjMXbZXgTeGfNtihh2lNxJO8cs5y2JjeOQivqDUXnQTfgPCBwQyhv/Bi0D4vPi9+ah7IotIkzXpjvZ9L256moX09dxZFsm3xWVPwbiA+nJMDtKGXGlof4bOoiNs26Ii5jxhSbDX9Hh3n8v6SED+7+G9smXIF7atC+u//G8N1W3vu0AG9X4AtG3vwAQ4E3E/5U24GM9TWYbRostmaanIiRb/r6Cdj3dntlUV6dRfGNS2cw7ZjKpPr676c/pqwgjx+dMs00Lt4T155yEP918lRD8Y7kwZf+x3DgMkQoXmuWQfLP41bQaY+fiVpU5mDOhBY2vN9Jp63EOE6dgCt/F4jtf/5eHa8/vDUsXHFExMFnT+1i3rWncc8Vr5n2e/TZk/jo1V10tnsJXI0IuxLF1E2wdrWirXlRwm/xuZn+2V9MxVyVlqD3t4Lf+Dspp5M9o4/m0/EL4/q1ah8eW3wNn75EWcHhtAWvWXbhKLTi6fTj9/W/RqRKLtga+btOV9jNYuQ54ZHbG6MfrUfXr2d0/XpqKo9l67TvMPKAYUn39T/nHBJ+n+rSb5UlThrb3Nz75nbufPnzKPE2+vN5cOY3+dEHj2PX3R5/aFKOPTgYFwpvGA3KHX6kk3c3K3ze7t5teRYmzhrBe+968NrjS/n2RFGZI8pTSEiE6H6608mo9+ooKnMYHucotPKvZ7+M8NZjBDuRgBuIvMXnRimFL8Z791sdbD/wHCr3bzYcxKy/6268zS3mX8lqpWr0/LinAr/VgX8AnBrtIytFHMDdnl554oEgF2yN/F0bhTp7Q04MdtqMU4up6NzCvPMPIr/IbryDCVprOj0+KkuNhbA0306+PToGnG+3Mn9GBUop05V5Ynlj/OHUFpThVRb8BNIAf33UxXz+yN+Z+tqrYREvOessKm9ejm3MGFAK25gxVN68nIMu+gY+rybPGbDFYlWcdPF0dmxuNPeiE2CzB24Crz+8tWcRjyEUljl24RRsedF/NrY8CwrzkEtPFBZoZn7xcCClUWscnY1M3/5XvHbjX3xnXinvnnQ79dO+AUpRP+0bvHvS7fz5uULenHAFdRXdDkt4wPeEVaw7Zjk1hTPM4/MpPtkIQm8I/U9lgpzwyCtm7aP2/RK0r1tAlNXPhGlfUnLSuJT68vk1X7/tNc6eM4bL501m+dpP41aXWXb2wUB8TZDbX/oMtzd5tRrbWs+E9gbun3k6fz3o5ITV+0rOOisuJe7TdYFwyznXHkbtF828/VgVwyryUxZhAEeBjeO+dSD/evbLtG4CEPAiQt5DbOzvlQfi0xuTwZZn4WsXzGTUyecyLmbw8at3nCbfVdHuUmw94N/g/CvZ+m4dXlfgOyUzYcnm7TC9SQhCf9LWlJlaSTkh5CVzyoG97Nk4DF+nFavDx6hD91Myp5z2Fjd7tu9n8qEjk+rLalE4bBbuX/clXp+mJN+GUspwGbNYwTWbIRpLKMOmwtWMT1k4/egDuf0nZ6T0nQG+3NhA8Qgn5eOKKBmZz9Z363jhtx/3fKABx59/UHLhlASEMoMOOnp03ONgOn1Hxwnjb2THViSO4Xu7/Hzyj5q4JwG/1cG2yWeH38du81vyAuGcnsI94qELfYzTYx4GTIWcEHLm30RJxw8pGlPP509VMmJ6OyVTA+1V7+9h3RNf8L2Vx1FY2nM2xNMf7qZ6nytc7rbZ5SXfbuWu8+f2OFNzTGk+xXu64irzbXUE4nMKOGHXBq6JqA9u1X4qH1lNy8xxUULV04h2V6eXXVv2Mev4sSil2PHRXvbVtpuKmi3Pgs1uMYy3OgqtvP7nrXg9iT1xR6EVhTLso6fMoGMXTkk8cBrT10kXT+8xNhjr/RthFs5JmN4YEugEA7BWT1vcQKvZhKV0262eNvy2fLTFlvQx/d7u92DzurufYLLBphy01eh3bfG5mVz1NHAevSU3hHz2IgCsr9yE1enD5y+As1bA7EVU7tgPQO22Fg48PH75t1huf+mzsIiHSLaA1n9OHk3DjlrswYG8Eq04zRWIz7eOymPpqdM4+Npf4TVYNCKyImBstkjswMfn79Xxj79W4fP6+fz9OioOKOadNdtMRTJ0IwDixDQUv/YmSLE0EtZUU6fMQi69TcMKef8P3bAuJY+/aIQTb5efzrYENWuUMs2MmfZFoOa6UbEww0JhabSDSdGxDJ5DbM1um8bZUpihnYCcSD8M4+1C3zwKdcKP4eSfAbD1nVpefWgLEPuobsyk658zHKRUwJcrE4c/zMQksjyAaf2SiGnyifox8mxteZaEnm4onRCMBThR/DpXJr30mCoZg7MwyZQ+rZm55cG4f7DKri+gszNuZijQPfM0yfbIomGqpCSqgFjRCcfT9uZbeGtro7al9L65OWWbkm632bAWFfXtOYaAraq0FNrb0Z5uxyKdchE5nX4YxpaHOvIyqJgOBP6533zks/DmZFJ6EpW77Qkzj7Ctyc2DS/7OpO1rqDC5MdoqK6P2N+vHyPP2dvlRFuMwQuyM1lTi14nq02QbyYRZAKx5Cl+XTjqlr7BAU7l/M6Pf7XYsQv9gED/rNVEhroEs0JWqTel8h74+x2C2NZFNmSAjHrlS6jTg14AV+L3WemWi/dP2yIHW116j+bHHGfebe/jjje+mLFDJFNAyo8fH++C1jH2kir3zJvLIE/Uf65knG2s28maTPTYbSTQpKVGeu8+jDa/BqPr3pUKikBP0mUeulLIC9wALgGrgfaXUM1rr9PLResDb2Ejbm2/iratL6NmaYbbcWCIRD91JJ3jHsnX6RYGsByOCgxxu5wg+nfE9Pp3xPZzeFg4/0knJWaeHdzMKn1isimMXTuGff/uC9uauuK5DIZB0Ys2J4te5iJlYJ7oRutt9LLhspsk1iM+YEYRcIhOhlaOAL7TW2wGUUo8CC4E+EfK8loCX2/XlFwn/oRMRudxYT0SuZFNubWL61ofZPmUhnY7hJFw0LSjqnfZS3vvUQsF7dWHhPOjo0XS5fWx4YQdt+9xYbQqLVfHOmm2GIh7KGDEKmyRLb47NNszGESJvdLEUlTkG1TUQhEgyMbNzLLAr4nN1sC0KpdRipdR6pdT6hoaGtE9mn3QgAJ7PPzKcZWi1JVdAK1nq77qb2mGzWHfMzbz19Tv4fOoiJm9bg6Mz+fU0jWZwNVa34fdrfvCbkzjmnMn4/cZPEkVljpwNgfQVBx09mpMunh6+YUdeI7OZp5n8mxCEbCMTHrmRWxoXeNdarwZWQyBGnu7J7FPngNJ0bf+cg74fPwBWObUkbdEzGoyo9o5l67QLw+lpXnshW6ddxOjad6irPDbpSn5tTW4eumEdxy6cwtSjRrHj472MmjgMi0Xx0WvV+AxyvHNpMLK/MfOuB1sYSRCSIRNCXg2Mj/g8DshMcqQBqvxA8kd0oTytQPQ/9Mu/38xXnzbh9fiw2Y3rZYNxit6o+vcNS5tuP3Ch4ezAxvLZTP/sL9G1tXuYCRjKqmnd10nbPjdHnjkp3G62v5A6EkIRhhqZEPL3galKqUnAbuAC4KLEh/SC/OFMPMMDc+In/xSPcOLu8HLvf71p6okZTcZ55YFPQRfAgRdHDVhunfxt04FNt3M4oxs2RCX7JxM793b5+eClrwA4YFZggYx0Y/2CIAiQgRi51toLXAW8BGwBHtdaf9Lbfk1RCk64Dg78RlTz5+/Vsen16vDnkPcbu7yZ6QzJ0BJjEfitDtM54IWFFtAaS2kpKMU4Ww3fOs/Blb+bz4LLZiYU4S6XF4tVsXtrIM4ucV1BEHpDRiYEaa2fB57PRF/JsL91GntvXcUBj3wda1GgroLZRJrYFXFSDlcoS1wBJYuviwPe/wuW4mIqrruO4eedG3VIMtPK/T4dN3lJ4rqCIKRDbs3sDOFx466qwrPrK6wzZgDJx5kL8/20u1J4EIny0jWOzn1M2b6G0fXrAzXGly/HYrcZ5iH3VEgq8kYjcV1BENIlJxaWiMXesQkAT1V3SVezUEaovWXtWqpOns8BGx7C4ktvENHpaeG4d2+MWmYs0arssWlyRsiApiAIvSUnhTxvamC5tq4vPoFNj8NdszjWuxKbip9ME6qD8sHdf8NbU8Oo+g2U791Enrs5EDKJK1GgMVv7p9NWYthutlo7BMT80luO6/FGIwiCkC45KeSW8TOx2P14Nr8Da38ILbs4qOAtTipeRZG1gVghbndZ2Dr529RVHEF7YSX1o45kyvY1nPzmVczc8mDUEmMnnj7CtNi7w208CSiyIJYZMqApCEJfkZNCvv8fH6P9sO+fX1H1ZDEtOwKVCw8qeJtLRy6myBYvuKFVY5pLAjNDS1sCMy1H16/n6xtv4TtndnDpLccx86w5TK56Oi78YvG5mbJ9DcoZvc6ncjqpWHJNjzYnmo0oCILQG3JusLNl7Vpqb/p5eP1Ob4eNmndLqXm3FFuBj4rZrbQ5Sw2PdTvKaC6dgsO9D2dnIwDW8nJG/eS6qMHKcbbdEDHZJ7IIfEVopfY0KuXJgKYgCH1Bzgl5/W0r0F2xq74EMku8HTZq3y+hcN4+2hkRd6zD3URzyYEMb67CElFa1vXxZqr/64dUXLeUvPHjqVhyDb4bb4qrUV0R3F8q5QmCkE3kXGjFuzfxYqXaZ2HSrr/HxaMtPjcT69/Gay+kjL1hEW984AF2XHghra+8ws7vfpeWtWspOessKm9ejm3MGFAK25gxKa/kIQiC0F/k1lJvQNVhU/F29PAgoRTWB18LT7DJz/NRsvM9zvjVRdgmHID2g91hpWXtWmqu/yn4uheZSGf5JUEQhP5gcCz1BlQcY6f2TV84Rm6ErbKSqRHx6HVX3sHGyq/xl9/txtW6IzxzUt11d5SIQ/xCyYIgCNlOzoVWSq5YRuUxHdgKvBjlfBtlkZR++9sAuFoDsfVQHZZqr/HiEonywgVBELKNnBNyZi+i5Oo7mfpdBzMuqGPMyRZs5SWgwFbgpXLpFXHe9PqXq+O68Xb52T71HMNTJMwLD05AYllp4HXT4736OoIgCL0l50IrAMxeFPgBSoI/1GzE++uTsM4qByIWiaipoe2EVYa1wjvtJSinE93ZGW5LmBe+6fHABCSPK/C5ZVfgc8gmQRCEASD3PHITWj/eTdWa0XRu/Sy8zqa3JrC+hcPdZHhMUZkzteyUV5d3i3gIjyvQLgiCMEDkpkdugOPguQC4fBNpvOvuKC97yvZn2DrtoqiVfkLT40uOPi75gc2W+BBNwnZBEIR+YNAIuX3sGKzDh9P58ea4wcpQtcJtk8/G7RyRer3vTY8HvW6TVM2Scb2wXBAEoXcMGiFXSuGcOJLOt5/FNnq0oZiPs9Uw9bVXU+s4Ni4eiz0f5t+UptWCIAi9Z9DEyAHyJ5bjbuyi/Hvnp13cKg6juHgIZymc+WsZ6BQEYUAZVEJefOppVB7VTMlhYzM3xd40/q3g+p0w5/xe2SwIgtBbBk1oBcB51Hycb7jw7fmM/NnfSj2MYkTJuECaoVH7hgfh78vB1RT4PP8m8c4FQeh3BpVH3vLqOqrWVPL5Vb9n26mn0fjQQ73vdP5NYM2LbrPnw9RT4Pkfg6sR0N055TJBSBCEfmbQCHnL2rXU/uxneF3dE38a7ryTlrVre9fx7EVwyLeDHxSUjIez/heqXgZfTDldjwueujx6xqfMBBUEoY/JueqHZlR9/RjDEre2Ai9Tv+vofdjD6wZbxPqay0oxTUeEgNc+5yL46C/Rg6X2/MCNQEIwgiCkiFn1w0HjkZvVKfd2WOPDHul4ybaYRZJ7yh33uGD9H2QmqCAIfc6gEfJANUSj9mCZ2pCAhvLCW3YRjm0/tRiWlRiLuqcT/nQuVP09un3+TQHvOh1adkmYRRCEjDFohLziGDvK6o9qU1Y/FbNbuxtaqk3ywoMhEqMBy4atsO016GqLPmT2okCIpGR8egbL4KggCBli0Ah5bJ1yW4GXyiNbKJkYIdol43quixIb+tjzSeB11Kz4fWcvgiWb4bz70vPOJcwiCEIG6FUeuVJqGXA50BBsukFr/XxvjUqL2YsouRpKXl0eDJsoogYjQ1Ppw9sTECn2ez4BWz6UTUp4biC5vhOdSxAEIQ0y4ZHfpbWeG/wZGBEPEfKQl7XAeauDYY+IlMHZiwJirnr42pEDmXs2Q8UMsFiTO7eRd27Ph/yyns8lCIKQBoNqZmcUocUnGrfBv+6DCcd2t299Aba/Bp3NmHruIQpGQOXs1M4LQe+8unvGJ8QX37JJwS1BEHpPJoT8KqXUJcB64Fqt9T6jnZRSi4HFABMmTMjAaZPEvR/e+y1MOAZKgwOTix7o3h4qUduyK+Cpn35HdI73tx8gZSJWMIojJPD2fFiwXPLJBUHoNT1OCFJK/R0wKtz9M+BdYC8Bl/ZmoFJr/f2eTtoXE4JM8XTCLWNg3o/g5P8G1z6wOiCvIHq/L9+Ch86C/OHgapbaKYIgZB1pTwjSWn9Daz3L4GeN1nqP1tqntfYD9wFH9YXxvcLuhPKpULc58Pmd38DKCQGBj6S1LuCRu/bRnV9+eSC//FcHZz5NUGvYWxV4TYRM8RcEoQd6NdiplIpcbv5cYHPvzOkjRs0KDFoC1H4EIw4MCHwkry4H7Y8/FmB/deZzvjc/CauOgLqPzfcxmrxkZEdfi73cTAQhq+lt1sovlVIfK6U2AScBSzJgU+YZPQv8XujqCAj5mLnx+6SaX95bXM2B13vnmYtjMos9JxL7TAhwsjcTQRAGjF4Ndmqtv5spQ/qUr/0Qvr4kED5pq4PKOfH7mNUdjyRTOd+bHodX/jui36A4QnRMPpnFns3E/oWfgNfVvc3sHD2R6GbS2/GD8EBztYxJCEIvGDQzOxMSygGv/SjwWmngkSdTOyVTOd/JeNqJzhfZbib2rqbUC3YZefDJ3EzSQTx9QcgYgzePPJZnlwRCK6ethNGHxG+Pm53ZQ355b0hWHI+9El68ProtZEfIm01UStfwHLvgtuAsVdc+8zz3kLDmDw/cFGIJ3UzS9ar70tMXhCHG0BHyne9A4xew6TF45x5jwYnM/+7Lx/5Ey8dF0h6sfFBcCa21wUYVyKaJvdFEYnOCvcBYgCG6PVT90agvjyswaUlZQfu62y327puJkfhDz9eqrzx9QRiCDI3QyqbHobEK/B6SfowPT/dvDrxm0ks0CuPEevxeN2x4CKadDtduDUz9VxbwdAR3SOCJa39QrJX5PtEHmG9yNQVE3OYM9GfNC3jph3w7+RBRJKHwjdk5pWSBIKTM0PDIX10eyFqJZCAf42On8ReMCPwcfF6gfdPjgcFKVxNU/6v76cAsPTISiw18XcEPmoSee6qctxr8Pnj6CrhjavcTQyyxXnXk7NmETxI9hK9kcFQQDBkaQp6Nj/GRYZytz8GjF8EdBwUXc44Qu/a98TVazFDW+BsWOj40kg7ezoCInhiM2ZuJOARE1lS8E9xUpp9pLsy9CeMIwiBnaIRWksn+GEjcbYAKijjEiZ3HFRDjRNjzzcVa+9JfzSiSlmp4Y2UPO6nuuHt4HKCnJwIF5dPgkyfNc97TCeMIwhBhaAh5MjHpgeS1m+lR7AzFOBgDD5XpNVutKGq7CpTUDZfVjYmj91Ryt8enmCQ871jyh8O+HcHQkcnye9n4VCUIWcLQCK2YlZbNlkfyZMSoZHzEwhgJvkNsGCZ0wzKryGgUd07Uj9niGemGb0I3J587ZkPM8nuJ0iAldi4McYaGkEPi0rIDTU+zSnsS4xDp3LCSKbkb24+RyCcTww8TjJmHbk5PLU68u8dl3L89H6aekjh2LiIvDAF6LGPbF/RrGdtcIHYgD4gTu2wSHyNx7HGZuwTf565ZKSyRF+wnFP4xy5UPncfophNaLUoQcgyzMrZDxyPPZrI99BOLmRef7s3ISHBNCYq418RLDxEqQxxL5ABprlxvQegB8ciFzNGbMEayueaZIjYcFPLUwfg7RH63/OGB/Vz7eve+ZFwgNFT1cmb77Sv7zK5HNrRD9tnUB2E9M49chFzIPqJEvQ8wG5g19PRDN5V+uLnkBGbXY4Db88ugqy1ij6s0CwAABVlJREFUMlwW2BTbbrGDozi6xlGKwp72CkGC0O+EyiOcd59x2qhZemSymGXXGFWMTCedclBjdj0GuN3VFCPiWWBTbLvfExzTyXy1TxFyIXuZvSg6/z2UD//N24wF/rz7zHPpBSHbyOCENhnsFLKbTKVH2vLNM1wEYaDI0IQ2EXIhNzETeLMMoJ5y1QVhIMhQmRARcmHwYSTyac1ITTCwBkMsa8UomyhbBxObkj9mIAdjM1gmRIRcGBqYTQ6acxF89JfUUhGHKtmWxpdLqYiJbMoAkn4oDB36Md9XEPoCySMXBEHIcSSPXBAEYZAiQi4IgpDjiJALgiDkOCLkgiAIOY4IuSAIQo4zIFkrSqkGYGeah5cDezNoTn8hdvc/uWq72N2/5JLdB2itR8Y2DoiQ9wal1Hqj9JtsR+zuf3LVdrG7f8lVuyOR0IogCEKOI0IuCIKQ4+SikK8eaAPSROzuf3LVdrG7f8lVu8PkXIxcEARBiCYXPXJBEAQhAhFyQRCEHCenhFwpdZpS6jOl1BdKqesH2h4zlFL3K6XqlVKbI9qWKaV2K6U2Bn9OH0gbjVBKOZVS/1JKfaSU+kQp9Ytge5lS6hWlVFXwdfhA22qEUsqqlPpQKfVs8HMuXPNSpdQTSqmtSqktSqljs/16K6WmRVzTjUqp/Uqpa3Lkel+tlNoc/Pu+JtiW1dc7GXImRq6UsgKfAwuAauB94EKt9acDapgBSqnjgTbgj1rrWcG2ZUCb1vqOgbQtEUopBRRqrduUUnbgH8DVwHlAk9Z6ZfAGOlxr/ZOBtNUIpdSPgCOAYVrrM3Pkmj8EvK21/r1SKg8oAG4gB643hP8vdwNHA5eRxddbKTULeBQ4CugCXgR+AFxOjlxvM3LJIz8K+EJrvV1r3UXgF7JwgG0yRGv9FpBzK/3qAG3Bj/bgjyZwnR8Ktj8EnDMA5iVEKTUOOAP4/UDbkixKqWHA8cAfALTWXVrrZnLgekcwH9imtU53pnZ/MgN4V2vdobX2Am8C55Jb19uQXBLysUDkoovVwbZc4iql1KZg6CUrH9+C4YmNQD3witb6PWCU1roWIPhaMZA2mnA3cB3gj2nP5ms+GWgAHgiGhH6vlCokN653iAuARyI+Z/P13gwcr5QaoZQqAE4HxpNb19uQXBJyZdCWG3GhAL8FpgBzgVrgzoE1xxittU9rPRcYBxwVfBzNapRSZwL1WusNMZuy/ZrbgMOA32qtDwXagawd+4klGAo6G/hrsCmrr7fWegtwG/AKgbDKR4B3QI3KELkk5NUE7p4hxgE1A2RLymit9wRF0g/cRyBUlLUEH/HfAE4D9iilKgGCr/UDaJoRxwFnK6V2EAi5nayU+nMOXPNqoDr41APwBAFhz/brHeKbwAda6z2QG3/jWus/aK0P01ofTyD8WUXuXG9TcknI3wemKqUmBT2BC4BnBtimpAn9oQQ5l8BjXlahlBqplCoNvs8HvgFsJXCdLw3udimwZmAsNEZr/VOt9Tit9UQCfxevaa2/k+3XXGtdB+xSSk0LNs0HPiXLr3cEFxIRVsn26w2glKoIvk4gMIj/CLlzvU2xDbQByaK19iqlrgJeAqzA/VrrTwbYLEOUUo8AJwLlSqlq4OfAiUqpuQTCQTuA/xgwA82pBB4KZiJYgMe11s8qpd4BHldK/TvwFfDtgTQyBX6ZA9f8v4CHg87JdgKZHxay/HoHY8wLiL6muXC9n1RKjQA8wJVa631KqZVk+fXuiZxJPxQEQRCMyaXQiiAIgmCACLkgCEKOI0IuCIKQ44iQC4Ig5Dgi5IIgCDmOCLkgCEKOI0IuCIKQ4/x/m0QnFu7DkUQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "None\n"
     ]
    }
   ],
   "source": [
    "print(\"loss = \", test.energy)\n",
    "print(\"method: \", mthd)\n",
    "print(\"method parameters: \", mthd_opt)\n",
    "print(\"execution time = \", (t1-t0)/60, \" min\")\n",
    "\n",
    "print(test.history.plot('energies', label='loss'))\n",
    "print(test.history.plot('angles', label=\"\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test\n",
    "\n",
    "Once trained, we have the optimal parameters for the classifier stored in `test.angles`. We run again the classifier with the test data set and with these parameters fixed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "success %:  90.5 %\n",
      "random success %:  49.1 %\n"
     ]
    }
   ],
   "source": [
    "test_set = 1000\n",
    "\n",
    "# initialize\n",
    "xval_test, yval_test, yval_rand, yval_real = [], [], [], []\n",
    "suc = 0 # success\n",
    "suc_rand = 0 # random success\n",
    "\n",
    "for i in range(test_set):\n",
    "    \n",
    "    # random test point\n",
    "    x = 2 * (np.random.rand(2)) - 1\n",
    "    \n",
    "    # state generated by the trained classifier\n",
    "    qc = qcircuit(x, param)\n",
    "    wfn_qc = tq.simulate(qc, variables=test.angles) \n",
    "        \n",
    "    if nclass == 2:\n",
    "        \n",
    "        # compute the fidelity respect to one of the label states, the |0>\n",
    "        f = abs(wfn_qc.inner(targ_wfn(0,nclass)))**2\n",
    "\n",
    "        y = 1\n",
    "        # if fidelity is >= 0.5, we conclude that this state belongs to |0> class\n",
    "        # (|1> class otherwise)\n",
    "        if f >= 0.5:\n",
    "            y = 0\n",
    "            \n",
    "        # check the real class of the data point\n",
    "        y_real = circle(random=False, x_input=x)\n",
    "        \n",
    "    else:\n",
    "        raise Exception(\"nclass = {} is not considered\".format(nclass))\n",
    "    \n",
    "    # compute success rate \n",
    "    if y == y_real:\n",
    "        suc = suc + 1\n",
    "        \n",
    "    # compute random success rate \n",
    "    yrand = np.random.randint(0, nclass-1)\n",
    "    if yrand == y_real:\n",
    "        suc_rand = suc_rand + 1\n",
    "        \n",
    "    xval_test.append(x)\n",
    "    yval_test.append(y)\n",
    "    yval_real.append(y_real)\n",
    "    \n",
    "print(\"success %: \", 100*suc/test_set,\"%\")\n",
    "print(\"random success %: \", 100*suc_rand/test_set,\"%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Print results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_data(x, y, nclass, fig=None, ax=None):\n",
    "    \"\"\"\n",
    "    Arg:\n",
    "        - x (array[tuple]): data points\n",
    "        - y (array[int]): data labels\n",
    "        - nclass (int): number of classes\n",
    "    Returns:\n",
    "        - Plot\n",
    "    \"\"\"    \n",
    "    if fig == None:\n",
    "        fig, ax = plt.subplots(1, 1, figsize=(5, 5))\n",
    "     \n",
    "    # colors and labels\n",
    "    col = [\"red\",\"blue\",\"green\",\"yellow\"]\n",
    "    lab = [0,1,2,3]\n",
    "    \n",
    "    for i in range(nclass):\n",
    "        ax.scatter(x[y == lab[i], 0], x[y == lab[i], 1], c=col[i], s=20, edgecolor=\"k\")\n",
    "    ax.set_xlabel(\"$x_1$\")\n",
    "    ax.set_ylabel(\"$x_2$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total execution time:  36.01548974911372  min.\n"
     ]
    }
   ],
   "source": [
    "xval_test = np.array(xval_test)\n",
    "yval_test = np.array(yval_test)\n",
    "yval_real = np.array(yval_real)\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(6, 3))\n",
    "\n",
    "plot_data(xval_test, yval_test, nclass, fig, axes[0])\n",
    "plot_data(xval_test, yval_real, nclass, fig, axes[1])\n",
    "\n",
    "axes[0].set_title(\"Single-qubit class. {} layers\".format(layers))\n",
    "axes[1].set_title(\"True test data\")\n",
    "fig.tight_layout(pad=0.5)\n",
    "plt.show()\n",
    "\n",
    "t2 = time.time()\n",
    "print(\"Total execution time: \", (t2-t0)/60,\" min.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Improvements and customization\n",
    "\n",
    "This tutorial just shows a simple classification example. It is constructed in a way that one can easily change the classification model and try more sophisticated problems comprising more classes. To do so, one should define the target states for >2 classes, i.e. include more vectors in the Bloch sphere.\n",
    "\n",
    "The single-qubit classifier circuit can also be modified to include higher dimensional data or to increase/reduce the number of parameters per layer.\n",
    "\n",
    "The cost function can also be improved. See for instance the weigthed fidelity cost function proposed in the main reference.\n",
    "\n",
    "Finally, the core of any variational algorithm is the minimization method. Tequila provides many methods besides the scipy ones. See the [optimizers tutorial](https://github.com/aspuru-guzik-group/tequila/blob/master/tutorials/Optimizer_Tutorial.ipynb) for more information.\n",
    "Notice also that the algorithm starts with a random initialization. It is well-known that random initialization in variational circuits leads to a barren-plateaus problem when computing the gradients. This problem can be avoided by providing a good initialization guess. \n",
    "\n",
    "Another possibility to play with expoloiting other Tequila modules is to use Phoenics for initial exploration and a gradient based optimizer with the best Phoenics results as starting point (see Phoenics documentation)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "tqenv",
   "language": "python",
   "name": "tqenv"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}