{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b1e0bbf3",
   "metadata": {},
   "source": [
    "# Reinforcement learning"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58b57fee",
   "metadata": {},
   "source": [
    "## Goal and perspectives\n",
    "\n",
    "This tutorial is mainly adapted from this article https://arxiv.org/pdf/2103.06294.pdf and inspired by the work done during the 2022 LOQCathon."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "8078725c",
   "metadata": {},
   "source": [
    "### Reinforcement learning\n",
    "\n",
    "Reinforcement learning is a machine learning framework where an agent tries to find the right actions to perform by interacting with an environment. This is modelled by an agent who is taking actions and receiving percepts from the environment which can be used to choose the next actions. At the end of an epoch (or a series of epochs), the environment rewards (or not) the agent according to the string of actions taken. From the reward, the agent learns and adapts their strategy for the next epochs.\n",
    "\n",
    "![reinforcement_learning.png](../_static/img/reinforcement-learning_reinforcement_learning.png)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "5a7f63da",
   "metadata": {},
   "source": [
    "In Quantum Reinforcement learning, the exchanged actions, percepts and rewards are now quantum states being exchanged between the environment and the agent. In their paper, the authors claimed to have found a quantum advantage in the time for training by making use of Grover's amplification method to reach good actions quicker, and the goal of this tutorial is to reproduce the main results of their paper:\n",
    "\n",
    "![results_paper.png](../_static/img/reinforcement-learning_results_paper.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f74c3b5",
   "metadata": {},
   "source": [
    "## Imports of packages and configuration of display"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7085c79d",
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import annotations\n",
    "\n",
    "import math\n",
    "\n",
    "from ipywidgets import FloatProgress\n",
    "from IPython.display import display\n",
    "\n",
    "import perceval as pcvl\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from perceval.components.unitary_components import Unitary, BS, PS\n",
    "from perceval.rendering import DisplayConfig, SymbSkin\n",
    "\n",
    "DisplayConfig.select_skin(SymbSkin)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "edc77d36",
   "metadata": {},
   "source": [
    "## Grover's algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c50e3403",
   "metadata": {},
   "source": [
    "We will now implement Grover's algorithm, firstly from a high-level picture (using unitaries) and then photonically (using Mach-Zehnder interferometers) in the same way that was done in the article."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e89e9be7",
   "metadata": {},
   "source": [
    "### Grover's algorithm in high-level picture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "83faf254",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's create a function that generates our circuit, given an angle xi\n",
    "\n",
    "def grover_circuit_unitaries(xi:float) -> pcvl.Circuit:\n",
    "    # Unitary to go from |00> to cos(xi)|10> + sin(xi)|01>\n",
    "    unitary_p = pcvl.Matrix(\n",
    "        np.array([[math.cos(xi), -math.sin(xi)], [math.sin(xi), math.cos(xi)]])\n",
    "    )\n",
    "    # Unitary for Hadamard gate\n",
    "    unitary_hadamard = pcvl.Matrix(1 / math.sqrt(2) * np.array([[1, 1], [1, -1]]))\n",
    "    # Unitary for environment interaction, that switches the phase of the good state\n",
    "    unitary_env = pcvl.Matrix(np.array([[0, -1], [-1, 0]]))\n",
    "    # Unitary of the reflection\n",
    "    unitary_reflection = pcvl.Matrix(\n",
    "        np.array(\n",
    "            [\n",
    "                [math.cos(2 * xi), math.sin(2 * xi)],\n",
    "                [math.sin(2 * xi), -math.cos(2 * xi)],\n",
    "            ]\n",
    "        )\n",
    "    )\n",
    "    \n",
    "    # We can now assemble our circuit\n",
    "    hadamard_component = Unitary(unitary_hadamard, \"H\")\n",
    "    circuit = pcvl.Circuit(4) // (1, Unitary(unitary_p, \"P\")) // (0, hadamard_component) // (2, hadamard_component) // (2, Unitary(unitary_env, \"env\"))\\\n",
    "              // (0, hadamard_component) // (2, hadamard_component) // (1, Unitary(unitary_reflection, \"reflection\"))\n",
    "    return circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "94b60295",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"\n",
       "     width=\"757.5\" height=\"281.25\" viewBox=\"-28.0 0 606.0 225.0\">\n",
       "<defs>\n",
       "</defs>\n",
       "<path d=\"M10,25.0 L25,25.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M10,75.0 L25,75.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M10,125.0 L25,125.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M10,175.0 L25,175.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M25,75 L125,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M25,125 L125,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M25,62.5 C25,62.5,25,50.0,37.5,50.0 L112.5,50.0 C125.0,50.0,125.0,62.5,125.0,62.5 L125.0,137.5 C125.0,137.5,125.0,150.0,112.5,150.0 L37.5,150.0 C25.0,150.0,25.0,137.5,25.0,137.5 L25.0,62.5\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightyellow\" />\n",
       "<text x=\"75\" y=\"100\" font-size=\"10\" text-anchor=\"middle\">P</text>\n",
       "<path d=\"M25,25.0 L125,25.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M125,25 L225,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M125,75 L225,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M125,12.5 C125,12.5,125,0.0,137.5,0.0 L212.5,0.0 C225.0,0.0,225.0,12.5,225.0,12.5 L225.0,87.5 C225.0,87.5,225.0,100.0,212.5,100.0 L137.5,100.0 C125.0,100.0,125.0,87.5,125.0,87.5 L125.0,12.5\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightyellow\" />\n",
       "<text x=\"175\" y=\"50\" font-size=\"10\" text-anchor=\"middle\">H</text>\n",
       "<path d=\"M25,175.0 L125,175.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M125,125 L225,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M125,175 L225,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M125,112.5 C125,112.5,125,100.0,137.5,100.0 L212.5,100.0 C225.0,100.0,225.0,112.5,225.0,112.5 L225.0,187.5 C225.0,187.5,225.0,200.0,212.5,200.0 L137.5,200.0 C125.0,200.0,125.0,187.5,125.0,187.5 L125.0,112.5\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightyellow\" />\n",
       "<text x=\"175\" y=\"150\" font-size=\"10\" text-anchor=\"middle\">H</text>\n",
       "<path d=\"M225,125 L325,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M225,175 L325,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M225,112.5 C225,112.5,225,100.0,237.5,100.0 L312.5,100.0 C325.0,100.0,325.0,112.5,325.0,112.5 L325.0,187.5 C325.0,187.5,325.0,200.0,312.5,200.0 L237.5,200.0 C225.0,200.0,225.0,187.5,225.0,187.5 L225.0,112.5\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightyellow\" />\n",
       "<text x=\"275\" y=\"150\" font-size=\"10\" text-anchor=\"middle\">env</text>\n",
       "<path d=\"M225,25 L325,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M225,75 L325,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M225,12.5 C225,12.5,225,0.0,237.5,0.0 L312.5,0.0 C325.0,0.0,325.0,12.5,325.0,12.5 L325.0,87.5 C325.0,87.5,325.0,100.0,312.5,100.0 L237.5,100.0 C225.0,100.0,225.0,87.5,225.0,87.5 L225.0,12.5\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightyellow\" />\n",
       "<text x=\"275\" y=\"50\" font-size=\"10\" text-anchor=\"middle\">H</text>\n",
       "<path d=\"M325,125 L425,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M325,175 L425,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M325,112.5 C325,112.5,325,100.0,337.5,100.0 L412.5,100.0 C425.0,100.0,425.0,112.5,425.0,112.5 L425.0,187.5 C425.0,187.5,425.0,200.0,412.5,200.0 L337.5,200.0 C325.0,200.0,325.0,187.5,325.0,187.5 L325.0,112.5\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightyellow\" />\n",
       "<text x=\"375\" y=\"150\" font-size=\"10\" text-anchor=\"middle\">H</text>\n",
       "<path d=\"M325,75.0 L425,75.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M425,75 L525,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M425,125 L525,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M425,62.5 C425,62.5,425,50.0,437.5,50.0 L512.5,50.0 C525.0,50.0,525.0,62.5,525.0,62.5 L525.0,137.5 C525.0,137.5,525.0,150.0,512.5,150.0 L437.5,150.0 C425.0,150.0,425.0,137.5,425.0,137.5 L425.0,62.5\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightyellow\" />\n",
       "<text x=\"475\" y=\"100\" font-size=\"10\" text-anchor=\"middle\">reflection</text>\n",
       "<path d=\"M325,25.0 L525,25.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M425,175.0 L525,175.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M525,25.0 L540,25.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M525,75.0 L540,75.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M525,125.0 L540,125.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M525,175.0 L540,175.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"550\" y=\"28.0\" font-size=\"6\" text-anchor=\"end\">0</text>\n",
       "<text x=\"550\" y=\"78.0\" font-size=\"6\" text-anchor=\"end\">1</text>\n",
       "<text x=\"550\" y=\"128.0\" font-size=\"6\" text-anchor=\"end\">2</text>\n",
       "<text x=\"550\" y=\"178.0\" font-size=\"6\" text-anchor=\"end\">3</text>\n",
       "<text x=\"0\" y=\"28.0\" font-size=\"6\" text-anchor=\"start\">0</text>\n",
       "<text x=\"0\" y=\"78.0\" font-size=\"6\" text-anchor=\"start\">1</text>\n",
       "<text x=\"0\" y=\"128.0\" font-size=\"6\" text-anchor=\"start\">2</text>\n",
       "<text x=\"0\" y=\"178.0\" font-size=\"6\" text-anchor=\"start\">3</text>\n",
       "</svg>"
      ],
      "text/plain": [
       "<drawsvg.drawing.Drawing at 0x7fb6bc36b760>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pcvl.pdisplay(grover_circuit_unitaries(math.pi/3))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01ddb6f0",
   "metadata": {},
   "source": [
    "One step of amplitude amplification in Grover's algorithm should rotate our state from a $\\xi$ angle to a $3\\xi$ angle from the loosing state to the winning state. Hence we can check the validity of our Grover's amplification algorithm by inputting a photon in the spatial mode 1 and detecting at spatial mode 2. This should follow a $\\sin(3\\xi)^2$ distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d1f06163",
   "metadata": {},
   "outputs": [],
   "source": [
    "xis = np.linspace(0, math.pi/2, 100)\n",
    "results = []\n",
    "for xi in xis:\n",
    "    circuit = grover_circuit_unitaries(xi)\n",
    "    backend = pcvl.BackendFactory.get_backend()\n",
    "    backend.set_circuit(circuit)\n",
    "    input_state = pcvl.BasicState([0, 1, 0, 0])\n",
    "    backend.set_input_state(input_state)\n",
    "    results.append(backend.probability(pcvl.BasicState([0, 0, 1, 0])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "09fc599f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb6bc1d2140>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xis, results, \"-o\", label=\"Simulation\")\n",
    "plt.plot(xis, np.sin((3*xis)) ** 2, \"--\", label=\"Theoretical\")\n",
    "plt.title(\"Probability after Grover's amplification\")\n",
    "plt.xlabel(\"$\\\\xi$\")\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.grid()\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ebd4183",
   "metadata": {},
   "source": [
    "### Designing the circuit with Mach-Zehnder interferometers"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "a46700fb",
   "metadata": {},
   "source": [
    "In the article they have used Mach-Zehnder interferometers (see below) to realize all the circuits.\n",
    "\n",
    "![mzi.png](../_static/img/reinforcement-learning_mzi.png)\n",
    "\n",
    "\n",
    "We want to perform the following unitary transformation (equation A.19 in the paper)\n",
    "\n",
    "$$U_{\\theta,\\varphi} = \\begin{pmatrix}e^{i\\varphi}\\sin\\left(\\frac{\\theta}{2}\\right) & e^{i\\varphi}\\cos\\left(\\frac{\\theta}{2}\\right)\\\\ \\cos\\left(\\frac{\\theta}{2}\\right) & -\\sin\\left(\\frac{\\theta}{2}\\right) \\end{pmatrix}$$\n",
    "\n",
    "However taking the MZI as shown and using the Rx convention for beam splitters yields the following matrix (see documentation [here](https://perceval.quandela.net/docs/components.html#beam-splitter)).\n",
    "\n",
    "\n",
    "$$ie^{i\\frac{\\theta}{2}}\\begin{pmatrix}e^{i\\varphi}\\sin\\left(\\frac{\\theta}{2}\\right) & e^{i\\varphi}\\cos\\left(\\frac{\\theta}{2}\\right)\\\\ \\cos\\left(\\frac{\\theta}{2}\\right) & -\\sin\\left(\\frac{\\theta}{2}\\right) \\end{pmatrix}$$\n",
    "\n",
    "To remove this global phase effect, we use phase shifters with angle $\\theta_2$ to be $-\\frac \\pi 2 - \\frac \\theta 2$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9cc0419f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def mzi(name:str, theta:float | pcvl.Parameter, phi:float | pcvl.Parameter, theta_2:float | pcvl.Parameter) -> pcvl.Circuit:\n",
    "    # For the mzi to be in the right shape:\n",
    "    #   theta_2 should be set to '- pi/2 - theta/2'\n",
    "    #   however we cannot pass a symbolic expression to the input of PS\n",
    "    #   so we need to define a third angle theta_2 that we will set to '- pi/2 - theta/2' later on\n",
    "    return (\n",
    "        pcvl.Circuit(2, name=name)\n",
    "        .add(0, BS())\n",
    "        .add(0, PS(theta))\n",
    "        .add(0, BS())\n",
    "        .add(0, PS(phi))\n",
    "        .add(0, PS(theta_2))\n",
    "        .add(1, PS(theta_2))\n",
    "    )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "79a8d2a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"\n",
       "     width=\"570.0\" height=\"156.25\" viewBox=\"-28.0 0 456.0 125.0\">\n",
       "<defs>\n",
       "</defs>\n",
       "<path d=\"M10,25.0 L25,25.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M10,75.0 L25,75.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M37.9442,25.0002 C51.653800000000004,25.0002,51.5923,50.0,65.3019,50.0 M65.3038,50.0 C51.59219999999999,50.0,51.6538,74.9998,37.94409999999999,74.9998 M65.3038,49.99999999999999 L87.1884,49.99999999999999 M87.1884,49.99999999999999 C100.9,49.99999999999999,100.83840000000001,25.000199999999992,114.5481,25.000199999999992 M87.1884,49.99999999999999 C100.9,49.99999999999999,100.83840000000001,74.9998,114.5481,74.9998 M25.0,24.999999999999993 L38.0,24.999999999999993 M38.0019,74.9998 L25.0,74.9998 M112.6453,74.9998 L125.0,74.9998 M112.1944,24.999799999999993 L125.0,24.999799999999993\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"75\" y=\"38\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M97,53 L107,53 L107,63 L97,63 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"102\" y=\"60\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M125,25 L145,25 M155,25 L175,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M140,35 L160,35 L160,15 L140,15 L140,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"150\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=theta_t</text>\n",
       "<path d=\"M125,75.0 L175,75.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M187.9442,25.0002 C201.6538,25.0002,201.5923,50.0,215.3019,50.0 M215.3038,50.0 C201.5922,50.0,201.6538,74.9998,187.9441,74.9998 M215.3038,49.99999999999999 L237.1884,49.99999999999999 M237.1884,49.99999999999999 C250.9,49.99999999999999,250.8384,25.000199999999992,264.5481,25.000199999999992 M237.18839999999997,49.99999999999999 C250.89999999999998,49.99999999999999,250.83839999999998,74.9998,264.5481,74.9998 M174.99999999999997,24.999999999999993 L187.99999999999997,24.999999999999993 M188.00189999999998,74.9998 L174.99999999999997,74.9998 M262.64529999999996,74.9998 L274.99999999999994,74.9998 M262.1944,24.999799999999993 L275.0,24.999799999999993\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"225\" y=\"38\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M247,53 L257,53 L257,63 L247,63 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"252\" y=\"60\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M275,25 L295,25 M305,25 L325,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M290,35 L310,35 L310,15 L290,15 L290,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"300\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=phi_t</text>\n",
       "<path d=\"M325,25 L345,25 M355,25 L375,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M340,35 L360,35 L360,15 L340,15 L340,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"350\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=theta_2</text>\n",
       "<path d=\"M275,75 L295,75 M305,75 L325,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M290,85 L310,85 L310,65 L290,65 L290,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"300\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=theta_2</text>\n",
       "<path d=\"M325,75.0 L375,75.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M375,25.0 L390,25.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M375,75.0 L390,75.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"400\" y=\"28.0\" font-size=\"6\" text-anchor=\"end\">0</text>\n",
       "<text x=\"400\" y=\"78.0\" font-size=\"6\" text-anchor=\"end\">1</text>\n",
       "<text x=\"0\" y=\"28.0\" font-size=\"6\" text-anchor=\"start\">0</text>\n",
       "<text x=\"0\" y=\"78.0\" font-size=\"6\" text-anchor=\"start\">1</text>\n",
       "</svg>"
      ],
      "text/plain": [
       "<drawsvg.drawing.Drawing at 0x7fb64c0447c0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_t = pcvl.P(\"theta_t\")\n",
    "phi_t = pcvl.P(\"phi_t\")\n",
    "theta_2 = pcvl.P(\"theta_2\")\n",
    "\n",
    "pcvl.pdisplay(mzi(\"test\", theta_t, phi_t, theta_2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f282446",
   "metadata": {},
   "source": [
    "#### Implementing the gates with MZI"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1227b4b9",
   "metadata": {},
   "source": [
    "##### Hadamard\n",
    "\n",
    "For the Hadamard, we want $\\theta$ and $\\varphi$ such that\n",
    "\n",
    "$$\\begin{pmatrix}e^{i\\varphi}\\sin\\left(\\frac{\\theta}{2}\\right) & e^{i\\varphi}\\cos\\left(\\frac{\\theta}{2}\\right)\\\\ \\cos\\left(\\frac{\\theta}{2}\\right) & -\\sin\\left(\\frac{\\theta}{2}\\right) \\end{pmatrix} = \\frac{1}{\\sqrt{2}}\\begin{pmatrix}1 & 1\\\\ 1 & -1 \\end{pmatrix}$$\n",
    "\n",
    "so we set $\\theta = \\frac{\\pi}{2}$ and $\\varphi = 0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "5edc592f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.707106781186547 - 1.11022302462516 \\cdot 10^{-16} i & \\frac{i \\left(-3.33066907387547 \\cdot 10^{-16} - 1.4142135623731 i\\right)}{2}\\\\\\frac{i \\left(-3.33066907387547 \\cdot 10^{-16} - 1.4142135623731 i\\right)}{2} & -0.707106781186547 + 1.11022302462516 \\cdot 10^{-16} i\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hadamard = mzi(\"H\", math.pi/2, 0, -math.pi/2 - math.pi/4)\n",
    "\n",
    "pcvl.pdisplay(hadamard.U)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5ce938e",
   "metadata": {},
   "source": [
    "##### Environment\n",
    "For the environment, we want a matrix of the form\n",
    "\n",
    "$$\\begin{pmatrix}e^{i\\varphi}\\sin\\left(\\frac{\\theta}{2}\\right) & e^{i\\varphi}\\cos\\left(\\frac{\\theta}{2}\\right)\\\\ \\cos\\left(\\frac{\\theta}{2}\\right) & -\\sin\\left(\\frac{\\theta}{2}\\right) \\end{pmatrix} = \\begin{pmatrix}0 & -1\\\\ -1 & 0 \\end{pmatrix}$$\n",
    "\n",
    "which gives $\\theta = -2\\pi$ and $\\varphi=0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5a76c917",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.22464679914735 \\cdot 10^{-16} & \\frac{i \\left(3.67394039744206 \\cdot 10^{-16} + 2.0 i\\right)}{2}\\\\\\frac{i \\left(3.67394039744206 \\cdot 10^{-16} + 2.0 i\\right)}{2} & -1.22464679914735 \\cdot 10^{-16}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "env = mzi(\"U_E\", -2 * math.pi, 0, -math.pi/2 + math.pi)\n",
    "\n",
    "pcvl.pdisplay(env.U)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c740108",
   "metadata": {},
   "source": [
    "##### Preparation of state\n",
    "\n",
    "For the preparation of the state, we want a matrix of the form\n",
    "\n",
    "\n",
    "$$\\begin{pmatrix}e^{i\\varphi}\\sin\\left(\\frac{\\theta}{2}\\right) & e^{i\\varphi}\\cos\\left(\\frac{\\theta}{2}\\right)\\\\ \\cos\\left(\\frac{\\theta}{2}\\right) & -\\sin\\left(\\frac{\\theta}{2}\\right) \\end{pmatrix} = \\begin{pmatrix}\\cos(\\xi) & -\\sin(\\xi)\\\\ \\sin(\\xi) & \\cos(\\xi) \\end{pmatrix}$$\n",
    "\n",
    "which gives $\\theta = \\pi - 2\\xi$ and $\\varphi=0$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "30243876",
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_prep = pcvl.P(\"theta_prep\") # We will set it to pi - 2*xi later\n",
    "theta2_prep = pcvl.P(\"theta2_prep\") # We will set it to -pi/2 - pi/2 + xi = -pi + xi later as we cannot pass symbolic expression to the function mzi\n",
    "state_prep = mzi(\"U_p\", theta_prep, 0, theta2_prep)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6905688f",
   "metadata": {},
   "source": [
    "##### Reflection\n",
    "\n",
    "For the reflection, we want a matrix of the form \n",
    "\n",
    "$$\\begin{pmatrix}e^{i\\varphi}\\sin\\left(\\frac{\\theta}{2}\\right) & e^{i\\varphi}\\cos\\left(\\frac{\\theta}{2}\\right)\\\\ \\cos\\left(\\frac{\\theta}{2}\\right) & -\\sin\\left(\\frac{\\theta}{2}\\right) \\end{pmatrix} = \\begin{pmatrix}\\cos(2\\xi) & \\sin(2\\xi)\\\\ \\sin(2\\xi) & -\\cos(2\\xi) \\end{pmatrix}$$\n",
    "\n",
    "which gives $\\theta = \\pi - 4\\xi$ and $\\varphi=0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a640d216",
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_ref = pcvl.P(\"theta_ref\") # We will set it to pi - 4*xi later\n",
    "theta2_ref = pcvl.P(\"theta2_ref\") # We will set it to -pi/2 - pi/2 + 2xi = -pi + 2xi later as we cannot pass symbolic expression to the function mzi\n",
    "ref = mzi(\"U_ref\", theta_ref, 0, theta2_ref)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0e532b8",
   "metadata": {},
   "source": [
    "### Grover's algorithm with MZI"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3acb6e44",
   "metadata": {},
   "source": [
    "We now implement again Grover's algorithm with MZI implementation as a sanity check for the definitions of the gates we chose."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5029c0f7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"\n",
       "     width=\"2320.0\" height=\"281.25\" viewBox=\"-28.0 0 1856.0 225.0\">\n",
       "<defs>\n",
       "</defs>\n",
       "<path d=\"M10,25.0 L25,25.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M10,75.0 L25,75.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M10,125.0 L25,125.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M10,175.0 L25,175.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M27,52 L373,52 L373,148 L27,148 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"29\" y=\"155\" font-size=\"8\" text-anchor=\"start\">U_P</text>\n",
       "<path d=\"M37.9442,75.0002 C51.653800000000004,75.0002,51.5923,100.0,65.3019,100.0 M65.3038,100.0 C51.59219999999999,100.0,51.6538,124.9998,37.94409999999999,124.9998 M65.3038,100.0 L87.1884,100.0 M87.1884,100.0 C100.9,100.0,100.83840000000001,75.0002,114.5481,75.0002 M87.1884,100.0 C100.9,100.0,100.83840000000001,124.9998,114.5481,124.9998 M25.0,75.0 L38.0,75.0 M38.0019,124.9998 L25.0,124.9998 M112.6453,124.9998 L125.0,124.9998 M112.1944,74.9998 L125.0,74.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"75\" y=\"88\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M97,103 L107,103 L107,113 L97,113 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"102\" y=\"110\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M125,75 L145,75 M155,75 L175,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M140,85 L160,85 L160,65 L140,65 L140,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"150\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=theta_prep</text>\n",
       "<path d=\"M125,125.0 L175,125.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M187.9442,75.0002 C201.6538,75.0002,201.5923,100.0,215.3019,100.0 M215.3038,100.0 C201.5922,100.0,201.6538,124.9998,187.9441,124.9998 M215.3038,100.0 L237.1884,100.0 M237.1884,100.0 C250.9,100.0,250.8384,75.0002,264.5481,75.0002 M237.18839999999997,100.0 C250.89999999999998,100.0,250.83839999999998,124.9998,264.5481,124.9998 M174.99999999999997,75.0 L187.99999999999997,75.0 M188.00189999999998,124.9998 L174.99999999999997,124.9998 M262.64529999999996,124.9998 L274.99999999999994,124.9998 M262.1944,74.9998 L275.0,74.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"225\" y=\"88\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M247,103 L257,103 L257,113 L247,113 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"252\" y=\"110\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M275,75 L295,75 M305,75 L325,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M290,85 L310,85 L310,65 L290,65 L290,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"300\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M325,75 L345,75 M355,75 L375,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M340,85 L360,85 L360,65 L340,65 L340,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"350\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=theta2_prep</text>\n",
       "<path d=\"M275,125 L295,125 M305,125 L325,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M290,135 L310,135 L310,115 L290,115 L290,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"300\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=theta2_prep</text>\n",
       "<path d=\"M25,25.0 L375,25.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M325,125.0 L375,125.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M377,2 L723,2 L723,98 L377,98 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"379\" y=\"105\" font-size=\"8\" text-anchor=\"start\">H</text>\n",
       "<path d=\"M387.9442,25.0002 C401.65380000000005,25.0002,401.5923,50.0,415.30190000000005,50.0 M415.3038,50.0 C401.59220000000005,50.0,401.65380000000005,74.9998,387.94410000000005,74.9998 M415.3038,49.99999999999999 L437.1884,49.99999999999999 M437.1884,49.99999999999999 C450.9,49.99999999999999,450.8384,25.000199999999992,464.5481,25.000199999999992 M437.1884,49.99999999999999 C450.9,49.99999999999999,450.8384,74.9998,464.5481,74.9998 M375.0,24.999999999999993 L388.0,24.999999999999993 M388.0019,74.9998 L375.0,74.9998 M462.6453,74.9998 L475.0,74.9998 M462.1944,24.999799999999993 L475.0,24.999799999999993\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"425\" y=\"38\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M447,53 L457,53 L457,63 L447,63 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"452\" y=\"60\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M475,25 L495,25 M505,25 L525,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M490,35 L510,35 L510,15 L490,15 L490,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"500\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M475,75.0 L525,75.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M537.9442,25.0002 C551.6538,25.0002,551.5923,50.0,565.3019,50.0 M565.3038,50.0 C551.5922,50.0,551.6538,74.9998,537.9441,74.9998 M565.3038,49.99999999999999 L587.1884,49.99999999999999 M587.1884,49.99999999999999 C600.9,49.99999999999999,600.8384,25.000199999999992,614.5481,25.000199999999992 M587.1884,49.99999999999999 C600.9,49.99999999999999,600.8384,74.9998,614.5481,74.9998 M525.0,24.999999999999993 L538.0,24.999999999999993 M538.0019,74.9998 L525.0,74.9998 M612.6453,74.9998 L625.0,74.9998 M612.1944,24.999799999999993 L625.0,24.999799999999993\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"575\" y=\"38\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M597,53 L607,53 L607,63 L597,63 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"602\" y=\"60\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M625,25 L645,25 M655,25 L675,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M640,35 L660,35 L660,15 L640,15 L640,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"650\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M675,25 L695,25 M705,25 L725,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M690,35 L710,35 L710,15 L690,15 L690,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"700\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M625,75 L645,75 M655,75 L675,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M640,85 L660,85 L660,65 L640,65 L640,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"650\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M675,75.0 L725,75.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M377,102 L723,102 L723,198 L377,198 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"379\" y=\"205\" font-size=\"8\" text-anchor=\"start\">H</text>\n",
       "<path d=\"M25,175.0 L375,175.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M387.9442,125.0002 C401.65380000000005,125.0002,401.5923,150.0,415.30190000000005,150.0 M415.3038,150.0 C401.59220000000005,150.0,401.65380000000005,174.9998,387.94410000000005,174.9998 M415.3038,150.0 L437.1884,150.0 M437.1884,150.0 C450.9,150.0,450.8384,125.0002,464.5481,125.0002 M437.1884,150.0 C450.9,150.0,450.8384,174.9998,464.5481,174.9998 M375.0,125.0 L388.0,125.0 M388.0019,174.9998 L375.0,174.9998 M462.6453,174.9998 L475.0,174.9998 M462.1944,124.9998 L475.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"425\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M447,153 L457,153 L457,163 L447,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"452\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M475,125 L495,125 M505,125 L525,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M490,135 L510,135 L510,115 L490,115 L490,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"500\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M475,175.0 L525,175.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M537.9442,125.0002 C551.6538,125.0002,551.5923,150.0,565.3019,150.0 M565.3038,150.0 C551.5922,150.0,551.6538,174.9998,537.9441,174.9998 M565.3038,150.0 L587.1884,150.0 M587.1884,150.0 C600.9,150.0,600.8384,125.0002,614.5481,125.0002 M587.1884,150.0 C600.9,150.0,600.8384,174.9998,614.5481,174.9998 M525.0,125.0 L538.0,125.0 M538.0019,174.9998 L525.0,174.9998 M612.6453,174.9998 L625.0,174.9998 M612.1944,124.9998 L625.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"575\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M597,153 L607,153 L607,163 L597,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"602\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M625,125 L645,125 M655,125 L675,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M640,135 L660,135 L660,115 L640,115 L640,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"650\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M675,125 L695,125 M705,125 L725,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M690,135 L710,135 L710,115 L690,115 L690,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"700\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M625,175 L645,175 M655,175 L675,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M640,185 L660,185 L660,165 L640,165 L640,185\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"650\" y=\"194\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M675,175.0 L725,175.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M727,102 L1073,102 L1073,198 L727,198 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"729\" y=\"205\" font-size=\"8\" text-anchor=\"start\">U_E</text>\n",
       "<path d=\"M737.9442,125.0002 C751.6538,125.0002,751.5923,150.0,765.3019,150.0 M765.3038,150.0 C751.5922,150.0,751.6538,174.9998,737.9441,174.9998 M765.3038,150.0 L787.1884,150.0 M787.1884,150.0 C800.9,150.0,800.8384,125.0002,814.5481,125.0002 M787.1884,150.0 C800.9,150.0,800.8384,174.9998,814.5481,174.9998 M725.0,125.0 L738.0,125.0 M738.0019,174.9998 L725.0,174.9998 M812.6453,174.9998 L825.0,174.9998 M812.1944,124.9998 L825.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"775\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M797,153 L807,153 L807,163 L797,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"802\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M825,125 L845,125 M855,125 L875,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M840,135 L860,135 L860,115 L840,115 L840,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"850\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=2*pi</text>\n",
       "<path d=\"M825,175.0 L875,175.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M887.9442,125.0002 C901.6538,125.0002,901.5923,150.0,915.3019,150.0 M915.3038,150.0 C901.5922,150.0,901.6538,174.9998,887.9441,174.9998 M915.3038,150.0 L937.1884,150.0 M937.1884,150.0 C950.9,150.0,950.8384,125.0002,964.5481,125.0002 M937.1884,150.0 C950.9,150.0,950.8384,174.9998,964.5481,174.9998 M875.0,125.0 L888.0,125.0 M888.0019,174.9998 L875.0,174.9998 M962.6453,174.9998 L975.0,174.9998 M962.1944,124.9998 L975.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"925\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M947,153 L957,153 L957,163 L947,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"952\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M975,125 L995,125 M1005,125 L1025,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M990,135 L1010,135 L1010,115 L990,115 L990,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1000\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M1025,125 L1045,125 M1055,125 L1075,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1040,135 L1060,135 L1060,115 L1040,115 L1040,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1050\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M975,175 L995,175 M1005,175 L1025,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M990,185 L1010,185 L1010,165 L990,165 L990,185\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1000\" y=\"194\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M1025,175.0 L1075,175.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M727,2 L1073,2 L1073,98 L727,98 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"729\" y=\"105\" font-size=\"8\" text-anchor=\"start\">H</text>\n",
       "<path d=\"M737.9442,25.0002 C751.6538,25.0002,751.5923,50.0,765.3019,50.0 M765.3038,50.0 C751.5922,50.0,751.6538,74.9998,737.9441,74.9998 M765.3038,49.99999999999999 L787.1884,49.99999999999999 M787.1884,49.99999999999999 C800.9,49.99999999999999,800.8384,25.000199999999992,814.5481,25.000199999999992 M787.1884,49.99999999999999 C800.9,49.99999999999999,800.8384,74.9998,814.5481,74.9998 M725.0,24.999999999999993 L738.0,24.999999999999993 M738.0019,74.9998 L725.0,74.9998 M812.6453,74.9998 L825.0,74.9998 M812.1944,24.999799999999993 L825.0,24.999799999999993\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"775\" y=\"38\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M797,53 L807,53 L807,63 L797,63 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"802\" y=\"60\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M825,25 L845,25 M855,25 L875,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M840,35 L860,35 L860,15 L840,15 L840,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"850\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M825,75.0 L875,75.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M887.9442,25.0002 C901.6538,25.0002,901.5923,50.0,915.3019,50.0 M915.3038,50.0 C901.5922,50.0,901.6538,74.9998,887.9441,74.9998 M915.3038,49.99999999999999 L937.1884,49.99999999999999 M937.1884,49.99999999999999 C950.9,49.99999999999999,950.8384,25.000199999999992,964.5481,25.000199999999992 M937.1884,49.99999999999999 C950.9,49.99999999999999,950.8384,74.9998,964.5481,74.9998 M875.0,24.999999999999993 L888.0,24.999999999999993 M888.0019,74.9998 L875.0,74.9998 M962.6453,74.9998 L975.0,74.9998 M962.1944,24.999799999999993 L975.0,24.999799999999993\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"925\" y=\"38\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M947,53 L957,53 L957,63 L947,63 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"952\" y=\"60\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M975,25 L995,25 M1005,25 L1025,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M990,35 L1010,35 L1010,15 L990,15 L990,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1000\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M1025,25 L1045,25 M1055,25 L1075,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1040,35 L1060,35 L1060,15 L1040,15 L1040,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1050\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M975,75 L995,75 M1005,75 L1025,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M990,85 L1010,85 L1010,65 L990,65 L990,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1000\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M1025,75.0 L1075,75.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1077,102 L1423,102 L1423,198 L1077,198 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1079\" y=\"205\" font-size=\"8\" text-anchor=\"start\">H</text>\n",
       "<path d=\"M1087.9442,125.0002 C1101.6537999999998,125.0002,1101.5922999999998,150.0,1115.3019,150.0 M1115.3038,150.0 C1101.5921999999998,150.0,1101.6537999999998,174.9998,1087.9441,174.9998 M1115.3038,150.0 L1137.1884,150.0 M1137.1884,150.0 C1150.9,150.0,1150.8384,125.0002,1164.5481,125.0002 M1137.1884,150.0 C1150.9,150.0,1150.8384,174.9998,1164.5481,174.9998 M1075.0,125.0 L1088.0,125.0 M1088.0019,174.9998 L1075.0,174.9998 M1162.6453,174.9998 L1175.0,174.9998 M1162.1944,124.9998 L1175.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"1125\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M1147,153 L1157,153 L1157,163 L1147,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1152\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M1175,125 L1195,125 M1205,125 L1225,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1190,135 L1210,135 L1210,115 L1190,115 L1190,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1200\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M1175,175.0 L1225,175.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1237.9442,125.0002 C1251.6537999999998,125.0002,1251.5922999999998,150.0,1265.3019,150.0 M1265.3038,150.0 C1251.5921999999998,150.0,1251.6537999999998,174.9998,1237.9441,174.9998 M1265.3038,150.0 L1287.1884,150.0 M1287.1884,150.0 C1300.9,150.0,1300.8384,125.0002,1314.5481,125.0002 M1287.1884,150.0 C1300.9,150.0,1300.8384,174.9998,1314.5481,174.9998 M1225.0,125.0 L1238.0,125.0 M1238.0019,174.9998 L1225.0,174.9998 M1312.6453,174.9998 L1325.0,174.9998 M1312.1944,124.9998 L1325.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"1275\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M1297,153 L1307,153 L1307,163 L1297,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1302\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M1325,125 L1345,125 M1355,125 L1375,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1340,135 L1360,135 L1360,115 L1340,115 L1340,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1350\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M1375,125 L1395,125 M1405,125 L1425,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1390,135 L1410,135 L1410,115 L1390,115 L1390,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1400\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M1325,175 L1345,175 M1355,175 L1375,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1340,185 L1360,185 L1360,165 L1340,165 L1340,185\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1350\" y=\"194\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M1375,175.0 L1425,175.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1427,52 L1773,52 L1773,148 L1427,148 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1429\" y=\"155\" font-size=\"8\" text-anchor=\"start\">U_REF</text>\n",
       "<path d=\"M1075,75.0 L1425,75.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1437.9442,75.0002 C1451.6537999999998,75.0002,1451.5922999999998,100.0,1465.3019,100.0 M1465.3038,100.0 C1451.5921999999998,100.0,1451.6537999999998,124.9998,1437.9441,124.9998 M1465.3038,100.0 L1487.1884,100.0 M1487.1884,100.0 C1500.9,100.0,1500.8384,75.0002,1514.5481,75.0002 M1487.1884,100.0 C1500.9,100.0,1500.8384,124.9998,1514.5481,124.9998 M1425.0,75.0 L1438.0,75.0 M1438.0019,124.9998 L1425.0,124.9998 M1512.6453,124.9998 L1525.0,124.9998 M1512.1944,74.9998 L1525.0,74.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"1475\" y=\"88\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M1497,103 L1507,103 L1507,113 L1497,113 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1502\" y=\"110\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M1525,75 L1545,75 M1555,75 L1575,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1540,85 L1560,85 L1560,65 L1540,65 L1540,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1550\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=theta_ref</text>\n",
       "<path d=\"M1525,125.0 L1575,125.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1587.9442,75.0002 C1601.6537999999998,75.0002,1601.5922999999998,100.0,1615.3019,100.0 M1615.3038,100.0 C1601.5921999999998,100.0,1601.6537999999998,124.9998,1587.9441,124.9998 M1615.3038,100.0 L1637.1884,100.0 M1637.1884,100.0 C1650.9,100.0,1650.8384,75.0002,1664.5481,75.0002 M1637.1884,100.0 C1650.9,100.0,1650.8384,124.9998,1664.5481,124.9998 M1575.0,75.0 L1588.0,75.0 M1588.0019,124.9998 L1575.0,124.9998 M1662.6453,124.9998 L1675.0,124.9998 M1662.1944,74.9998 L1675.0,74.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"1625\" y=\"88\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M1647,103 L1657,103 L1657,113 L1647,113 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1652\" y=\"110\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M1675,75 L1695,75 M1705,75 L1725,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1690,85 L1710,85 L1710,65 L1690,65 L1690,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1700\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M1725,75 L1745,75 M1755,75 L1775,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1740,85 L1760,85 L1760,65 L1740,65 L1740,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1750\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=theta2_ref</text>\n",
       "<path d=\"M1675,125 L1695,125 M1705,125 L1725,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1690,135 L1710,135 L1710,115 L1690,115 L1690,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1700\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=theta2_ref</text>\n",
       "<path d=\"M1075,25.0 L1775,25.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1725,125.0 L1775,125.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1425,175.0 L1775,175.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1775,25.0 L1790,25.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1775,75.0 L1790,75.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1775,125.0 L1790,125.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1775,175.0 L1790,175.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"1800\" y=\"28.0\" font-size=\"6\" text-anchor=\"end\">0</text>\n",
       "<text x=\"1800\" y=\"78.0\" font-size=\"6\" text-anchor=\"end\">1</text>\n",
       "<text x=\"1800\" y=\"128.0\" font-size=\"6\" text-anchor=\"end\">2</text>\n",
       "<text x=\"1800\" y=\"178.0\" font-size=\"6\" text-anchor=\"end\">3</text>\n",
       "<text x=\"0\" y=\"28.0\" font-size=\"6\" text-anchor=\"start\">0</text>\n",
       "<text x=\"0\" y=\"78.0\" font-size=\"6\" text-anchor=\"start\">1</text>\n",
       "<text x=\"0\" y=\"128.0\" font-size=\"6\" text-anchor=\"start\">2</text>\n",
       "<text x=\"0\" y=\"178.0\" font-size=\"6\" text-anchor=\"start\">3</text>\n",
       "</svg>"
      ],
      "text/plain": [
       "<drawsvg.drawing.Drawing at 0x7fb64bbe31f0>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit = pcvl.Circuit(4)\n",
    "circuit.add(1, state_prep).add(0, hadamard).add(2, hadamard).add(2, env).add(0, hadamard).add(2, hadamard).add(1, ref)\n",
    "\n",
    "pcvl.pdisplay(circuit, recursive=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "3d002e05",
   "metadata": {},
   "outputs": [],
   "source": [
    "results_mzis = []\n",
    "\n",
    "for xi in xis:\n",
    "    # Update values in the circuit\n",
    "    theta1 = math.pi - 2*xi #set the angle as explained above in 'Preparation of state'\n",
    "    theta_prep.set_value(theta1)\n",
    "    theta2_prep.set_value(-math.pi/2 - theta1/2)\n",
    "    \n",
    "    theta2 = math.pi - 4*xi #set the angle as explained above in 'Reflection'\n",
    "    theta_ref.set_value(theta2)\n",
    "    theta2_ref.set_value(-math.pi/2 - theta2/2)\n",
    "    \n",
    "    backend = pcvl.BackendFactory.get_backend()\n",
    "    backend.set_circuit(circuit)\n",
    "    input_state = pcvl.BasicState([0, 1, 0, 0])\n",
    "    backend.set_input_state(input_state)\n",
    "    results_mzis.append(backend.probability(pcvl.BasicState([0, 0, 1, 0])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "68692596",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb64bb92dd0>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xis, results, \"-o\", label=\"Simulation (Unitaries)\")\n",
    "plt.plot(xis, results_mzis, \"-o\", label=\"Simulation (MZIs)\")\n",
    "plt.plot(xis, np.sin((3*xis)) ** 2, \"--\", label=\"Theoretical\")\n",
    "plt.title(\"Probability after Grover's amplification\")\n",
    "plt.xlabel(\"$\\\\xi$\")\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.grid()\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f746dd6f",
   "metadata": {},
   "source": [
    "## Reproducing the results of the paper"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "630086db",
   "metadata": {},
   "source": [
    "### Classical circuit"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "8e07dd70",
   "metadata": {},
   "source": [
    "The classical circuit emulates the agent choosing a good action with probability $\\varepsilon = \\sin^2(\\xi)$. To this end, the operation $U_p |0_A0_R\\rangle = \\cos(\\xi)|0_A0_R\\rangle + \\sin(\\xi)|1_A0_R\\rangle$ is implemented putting the action state in a superposition with the corresponding amplitude. Then the interaction with the environment will make the second qubit switch only if the first qubit is in the state $|1_A\\rangle$, hence putting the reward qubit in the $|1_R\\rangle$ state.\n",
    "\n",
    "![classical_circuit.png](../_static/img/reinforcement-learning_classical_circuit.png)\n",
    "\n",
    "The detector D1, corresponding to $|0_A0_R\\rangle$, will click with probability $\\cos^2(\\xi) = 1-\\varepsilon$ and corresponds to no reward, whereas detector D2, corresponding to $|1_A1_R\\rangle$, will click with probability $\\sin^2(\\xi) = \\varepsilon$ and correspond to a rewarded action.\n",
    "\n",
    "Both operations $U_p$ and $U_e$ were already implemented as part of the Grover's algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "4fe0e455",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"\n",
       "     width=\"1007.5\" height=\"281.25\" viewBox=\"-28.0 0 806.0 225.0\">\n",
       "<defs>\n",
       "</defs>\n",
       "<path d=\"M10,25.0 L25,25.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M10,75.0 L25,75.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M10,125.0 L25,125.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M10,175.0 L25,175.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M27,52 L373,52 L373,148 L27,148 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"29\" y=\"155\" font-size=\"8\" text-anchor=\"start\">U_P</text>\n",
       "<path d=\"M37.9442,75.0002 C51.653800000000004,75.0002,51.5923,100.0,65.3019,100.0 M65.3038,100.0 C51.59219999999999,100.0,51.6538,124.9998,37.94409999999999,124.9998 M65.3038,100.0 L87.1884,100.0 M87.1884,100.0 C100.9,100.0,100.83840000000001,75.0002,114.5481,75.0002 M87.1884,100.0 C100.9,100.0,100.83840000000001,124.9998,114.5481,124.9998 M25.0,75.0 L38.0,75.0 M38.0019,124.9998 L25.0,124.9998 M112.6453,124.9998 L125.0,124.9998 M112.1944,74.9998 L125.0,74.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"75\" y=\"88\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M97,103 L107,103 L107,113 L97,113 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"102\" y=\"110\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M125,75 L145,75 M155,75 L175,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M140,85 L160,85 L160,65 L140,65 L140,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"150\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M125,125.0 L175,125.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M187.9442,75.0002 C201.6538,75.0002,201.5923,100.0,215.3019,100.0 M215.3038,100.0 C201.5922,100.0,201.6538,124.9998,187.9441,124.9998 M215.3038,100.0 L237.1884,100.0 M237.1884,100.0 C250.9,100.0,250.8384,75.0002,264.5481,75.0002 M237.18839999999997,100.0 C250.89999999999998,100.0,250.83839999999998,124.9998,264.5481,124.9998 M174.99999999999997,75.0 L187.99999999999997,75.0 M188.00189999999998,124.9998 L174.99999999999997,124.9998 M262.64529999999996,124.9998 L274.99999999999994,124.9998 M262.1944,74.9998 L275.0,74.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"225\" y=\"88\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M247,103 L257,103 L257,113 L247,113 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"252\" y=\"110\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M275,75 L295,75 M305,75 L325,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M290,85 L310,85 L310,65 L290,65 L290,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"300\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M325,75 L345,75 M355,75 L375,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M340,85 L360,85 L360,65 L340,65 L340,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"350\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=3*pi/2</text>\n",
       "<path d=\"M275,125 L295,125 M305,125 L325,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M290,135 L310,135 L310,115 L290,115 L290,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"300\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=3*pi/2</text>\n",
       "<path d=\"M25,25.0 L375,25.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M325,125.0 L375,125.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M377,102 L723,102 L723,198 L377,198 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"379\" y=\"205\" font-size=\"8\" text-anchor=\"start\">U_E</text>\n",
       "<path d=\"M25,175.0 L375,175.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M387.9442,125.0002 C401.65380000000005,125.0002,401.5923,150.0,415.30190000000005,150.0 M415.3038,150.0 C401.59220000000005,150.0,401.65380000000005,174.9998,387.94410000000005,174.9998 M415.3038,150.0 L437.1884,150.0 M437.1884,150.0 C450.9,150.0,450.8384,125.0002,464.5481,125.0002 M437.1884,150.0 C450.9,150.0,450.8384,174.9998,464.5481,174.9998 M375.0,125.0 L388.0,125.0 M388.0019,174.9998 L375.0,174.9998 M462.6453,174.9998 L475.0,174.9998 M462.1944,124.9998 L475.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"425\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M447,153 L457,153 L457,163 L447,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"452\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M475,125 L495,125 M505,125 L525,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M490,135 L510,135 L510,115 L490,115 L490,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"500\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=2*pi</text>\n",
       "<path d=\"M475,175.0 L525,175.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M537.9442,125.0002 C551.6538,125.0002,551.5923,150.0,565.3019,150.0 M565.3038,150.0 C551.5922,150.0,551.6538,174.9998,537.9441,174.9998 M565.3038,150.0 L587.1884,150.0 M587.1884,150.0 C600.9,150.0,600.8384,125.0002,614.5481,125.0002 M587.1884,150.0 C600.9,150.0,600.8384,174.9998,614.5481,174.9998 M525.0,125.0 L538.0,125.0 M538.0019,174.9998 L525.0,174.9998 M612.6453,174.9998 L625.0,174.9998 M612.1944,124.9998 L625.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"575\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M597,153 L607,153 L607,163 L597,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"602\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M625,125 L645,125 M655,125 L675,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M640,135 L660,135 L660,115 L640,115 L640,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"650\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M675,125 L695,125 M705,125 L725,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M690,135 L710,135 L710,115 L690,115 L690,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"700\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M625,175 L645,175 M655,175 L675,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M640,185 L660,185 L660,165 L640,165 L640,185\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"650\" y=\"194\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M675,175.0 L725,175.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M375,25.0 L725,25.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M375,75.0 L725,75.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M725,25.0 L740,25.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M725,75.0 L740,75.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M725,125.0 L740,125.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M725,175.0 L740,175.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"750\" y=\"28.0\" font-size=\"6\" text-anchor=\"end\">0</text>\n",
       "<text x=\"750\" y=\"78.0\" font-size=\"6\" text-anchor=\"end\">1</text>\n",
       "<text x=\"750\" y=\"128.0\" font-size=\"6\" text-anchor=\"end\">2</text>\n",
       "<text x=\"750\" y=\"178.0\" font-size=\"6\" text-anchor=\"end\">3</text>\n",
       "<text x=\"0\" y=\"28.0\" font-size=\"6\" text-anchor=\"start\">0</text>\n",
       "<text x=\"0\" y=\"78.0\" font-size=\"6\" text-anchor=\"start\">1</text>\n",
       "<text x=\"0\" y=\"128.0\" font-size=\"6\" text-anchor=\"start\">2</text>\n",
       "<text x=\"0\" y=\"178.0\" font-size=\"6\" text-anchor=\"start\">3</text>\n",
       "</svg>"
      ],
      "text/plain": [
       "<drawsvg.drawing.Drawing at 0x7fb6bc368f70>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classical_circuit = pcvl.Circuit(4)\n",
    "classical_circuit.add(1, state_prep).add(2, env) # circuit for classical strategy\n",
    "pcvl.pdisplay(classical_circuit, recursive=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d288dabc",
   "metadata": {},
   "source": [
    "### Quantum circuit"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "6fad7238",
   "metadata": {},
   "source": [
    "The quantum circuit performs a Grover's amplification step in order to get the state closer to a rewarded state. However, during this step, no reward is ever perceived and a classical round is still needed afterward to check if the state is rewarded or not.\n",
    "\n",
    "![quantum_circuit.png](../_static/img/reinforcement-learning_quantum_circuit.png)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "c3f95a3e",
   "metadata": {},
   "source": [
    "We will here, directly append the classical circuit (without state preparation) to the quantum circuit, so that the whole operation is done with one circuits. Note that we will count this as being 2 epochs to have a fair comparison with the classical strategy.\n",
    "\n",
    "![classical_quantum.png](../_static/img/reinforcement-learning_classical_quantum.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c1a8c795",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"\n",
       "     width=\"2757.5\" height=\"281.25\" viewBox=\"-28.0 0 2206.0 225.0\">\n",
       "<defs>\n",
       "</defs>\n",
       "<path d=\"M10,25.0 L25,25.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M10,75.0 L25,75.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M10,125.0 L25,125.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M10,175.0 L25,175.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M27,52 L373,52 L373,148 L27,148 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"29\" y=\"155\" font-size=\"8\" text-anchor=\"start\">U_P</text>\n",
       "<path d=\"M37.9442,75.0002 C51.653800000000004,75.0002,51.5923,100.0,65.3019,100.0 M65.3038,100.0 C51.59219999999999,100.0,51.6538,124.9998,37.94409999999999,124.9998 M65.3038,100.0 L87.1884,100.0 M87.1884,100.0 C100.9,100.0,100.83840000000001,75.0002,114.5481,75.0002 M87.1884,100.0 C100.9,100.0,100.83840000000001,124.9998,114.5481,124.9998 M25.0,75.0 L38.0,75.0 M38.0019,124.9998 L25.0,124.9998 M112.6453,124.9998 L125.0,124.9998 M112.1944,74.9998 L125.0,74.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"75\" y=\"88\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M97,103 L107,103 L107,113 L97,113 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"102\" y=\"110\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M125,75 L145,75 M155,75 L175,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M140,85 L160,85 L160,65 L140,65 L140,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"150\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M125,125.0 L175,125.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M187.9442,75.0002 C201.6538,75.0002,201.5923,100.0,215.3019,100.0 M215.3038,100.0 C201.5922,100.0,201.6538,124.9998,187.9441,124.9998 M215.3038,100.0 L237.1884,100.0 M237.1884,100.0 C250.9,100.0,250.8384,75.0002,264.5481,75.0002 M237.18839999999997,100.0 C250.89999999999998,100.0,250.83839999999998,124.9998,264.5481,124.9998 M174.99999999999997,75.0 L187.99999999999997,75.0 M188.00189999999998,124.9998 L174.99999999999997,124.9998 M262.64529999999996,124.9998 L274.99999999999994,124.9998 M262.1944,74.9998 L275.0,74.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"225\" y=\"88\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M247,103 L257,103 L257,113 L247,113 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"252\" y=\"110\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M275,75 L295,75 M305,75 L325,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M290,85 L310,85 L310,65 L290,65 L290,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"300\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M325,75 L345,75 M355,75 L375,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M340,85 L360,85 L360,65 L340,65 L340,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"350\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=3*pi/2</text>\n",
       "<path d=\"M275,125 L295,125 M305,125 L325,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M290,135 L310,135 L310,115 L290,115 L290,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"300\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=3*pi/2</text>\n",
       "<path d=\"M25,25.0 L375,25.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M325,125.0 L375,125.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M377,2 L723,2 L723,98 L377,98 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"379\" y=\"105\" font-size=\"8\" text-anchor=\"start\">H</text>\n",
       "<path d=\"M387.9442,25.0002 C401.65380000000005,25.0002,401.5923,50.0,415.30190000000005,50.0 M415.3038,50.0 C401.59220000000005,50.0,401.65380000000005,74.9998,387.94410000000005,74.9998 M415.3038,49.99999999999999 L437.1884,49.99999999999999 M437.1884,49.99999999999999 C450.9,49.99999999999999,450.8384,25.000199999999992,464.5481,25.000199999999992 M437.1884,49.99999999999999 C450.9,49.99999999999999,450.8384,74.9998,464.5481,74.9998 M375.0,24.999999999999993 L388.0,24.999999999999993 M388.0019,74.9998 L375.0,74.9998 M462.6453,74.9998 L475.0,74.9998 M462.1944,24.999799999999993 L475.0,24.999799999999993\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"425\" y=\"38\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M447,53 L457,53 L457,63 L447,63 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"452\" y=\"60\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M475,25 L495,25 M505,25 L525,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M490,35 L510,35 L510,15 L490,15 L490,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"500\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M475,75.0 L525,75.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M537.9442,25.0002 C551.6538,25.0002,551.5923,50.0,565.3019,50.0 M565.3038,50.0 C551.5922,50.0,551.6538,74.9998,537.9441,74.9998 M565.3038,49.99999999999999 L587.1884,49.99999999999999 M587.1884,49.99999999999999 C600.9,49.99999999999999,600.8384,25.000199999999992,614.5481,25.000199999999992 M587.1884,49.99999999999999 C600.9,49.99999999999999,600.8384,74.9998,614.5481,74.9998 M525.0,24.999999999999993 L538.0,24.999999999999993 M538.0019,74.9998 L525.0,74.9998 M612.6453,74.9998 L625.0,74.9998 M612.1944,24.999799999999993 L625.0,24.999799999999993\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"575\" y=\"38\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M597,53 L607,53 L607,63 L597,63 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"602\" y=\"60\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M625,25 L645,25 M655,25 L675,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M640,35 L660,35 L660,15 L640,15 L640,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"650\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M675,25 L695,25 M705,25 L725,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M690,35 L710,35 L710,15 L690,15 L690,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"700\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M625,75 L645,75 M655,75 L675,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M640,85 L660,85 L660,65 L640,65 L640,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"650\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M675,75.0 L725,75.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M377,102 L723,102 L723,198 L377,198 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"379\" y=\"205\" font-size=\"8\" text-anchor=\"start\">H</text>\n",
       "<path d=\"M25,175.0 L375,175.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M387.9442,125.0002 C401.65380000000005,125.0002,401.5923,150.0,415.30190000000005,150.0 M415.3038,150.0 C401.59220000000005,150.0,401.65380000000005,174.9998,387.94410000000005,174.9998 M415.3038,150.0 L437.1884,150.0 M437.1884,150.0 C450.9,150.0,450.8384,125.0002,464.5481,125.0002 M437.1884,150.0 C450.9,150.0,450.8384,174.9998,464.5481,174.9998 M375.0,125.0 L388.0,125.0 M388.0019,174.9998 L375.0,174.9998 M462.6453,174.9998 L475.0,174.9998 M462.1944,124.9998 L475.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"425\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M447,153 L457,153 L457,163 L447,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"452\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M475,125 L495,125 M505,125 L525,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M490,135 L510,135 L510,115 L490,115 L490,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"500\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M475,175.0 L525,175.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M537.9442,125.0002 C551.6538,125.0002,551.5923,150.0,565.3019,150.0 M565.3038,150.0 C551.5922,150.0,551.6538,174.9998,537.9441,174.9998 M565.3038,150.0 L587.1884,150.0 M587.1884,150.0 C600.9,150.0,600.8384,125.0002,614.5481,125.0002 M587.1884,150.0 C600.9,150.0,600.8384,174.9998,614.5481,174.9998 M525.0,125.0 L538.0,125.0 M538.0019,174.9998 L525.0,174.9998 M612.6453,174.9998 L625.0,174.9998 M612.1944,124.9998 L625.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"575\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M597,153 L607,153 L607,163 L597,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"602\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M625,125 L645,125 M655,125 L675,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M640,135 L660,135 L660,115 L640,115 L640,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"650\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M675,125 L695,125 M705,125 L725,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M690,135 L710,135 L710,115 L690,115 L690,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"700\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M625,175 L645,175 M655,175 L675,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M640,185 L660,185 L660,165 L640,165 L640,185\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"650\" y=\"194\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M675,175.0 L725,175.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M727,102 L1073,102 L1073,198 L727,198 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"729\" y=\"205\" font-size=\"8\" text-anchor=\"start\">U_E</text>\n",
       "<path d=\"M737.9442,125.0002 C751.6538,125.0002,751.5923,150.0,765.3019,150.0 M765.3038,150.0 C751.5922,150.0,751.6538,174.9998,737.9441,174.9998 M765.3038,150.0 L787.1884,150.0 M787.1884,150.0 C800.9,150.0,800.8384,125.0002,814.5481,125.0002 M787.1884,150.0 C800.9,150.0,800.8384,174.9998,814.5481,174.9998 M725.0,125.0 L738.0,125.0 M738.0019,174.9998 L725.0,174.9998 M812.6453,174.9998 L825.0,174.9998 M812.1944,124.9998 L825.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"775\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M797,153 L807,153 L807,163 L797,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"802\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M825,125 L845,125 M855,125 L875,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M840,135 L860,135 L860,115 L840,115 L840,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"850\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=2*pi</text>\n",
       "<path d=\"M825,175.0 L875,175.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M887.9442,125.0002 C901.6538,125.0002,901.5923,150.0,915.3019,150.0 M915.3038,150.0 C901.5922,150.0,901.6538,174.9998,887.9441,174.9998 M915.3038,150.0 L937.1884,150.0 M937.1884,150.0 C950.9,150.0,950.8384,125.0002,964.5481,125.0002 M937.1884,150.0 C950.9,150.0,950.8384,174.9998,964.5481,174.9998 M875.0,125.0 L888.0,125.0 M888.0019,174.9998 L875.0,174.9998 M962.6453,174.9998 L975.0,174.9998 M962.1944,124.9998 L975.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"925\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M947,153 L957,153 L957,163 L947,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"952\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M975,125 L995,125 M1005,125 L1025,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M990,135 L1010,135 L1010,115 L990,115 L990,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1000\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M1025,125 L1045,125 M1055,125 L1075,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1040,135 L1060,135 L1060,115 L1040,115 L1040,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1050\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M975,175 L995,175 M1005,175 L1025,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M990,185 L1010,185 L1010,165 L990,165 L990,185\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1000\" y=\"194\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M1025,175.0 L1075,175.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M727,2 L1073,2 L1073,98 L727,98 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"729\" y=\"105\" font-size=\"8\" text-anchor=\"start\">H</text>\n",
       "<path d=\"M737.9442,25.0002 C751.6538,25.0002,751.5923,50.0,765.3019,50.0 M765.3038,50.0 C751.5922,50.0,751.6538,74.9998,737.9441,74.9998 M765.3038,49.99999999999999 L787.1884,49.99999999999999 M787.1884,49.99999999999999 C800.9,49.99999999999999,800.8384,25.000199999999992,814.5481,25.000199999999992 M787.1884,49.99999999999999 C800.9,49.99999999999999,800.8384,74.9998,814.5481,74.9998 M725.0,24.999999999999993 L738.0,24.999999999999993 M738.0019,74.9998 L725.0,74.9998 M812.6453,74.9998 L825.0,74.9998 M812.1944,24.999799999999993 L825.0,24.999799999999993\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"775\" y=\"38\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M797,53 L807,53 L807,63 L797,63 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"802\" y=\"60\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M825,25 L845,25 M855,25 L875,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M840,35 L860,35 L860,15 L840,15 L840,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"850\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M825,75.0 L875,75.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M887.9442,25.0002 C901.6538,25.0002,901.5923,50.0,915.3019,50.0 M915.3038,50.0 C901.5922,50.0,901.6538,74.9998,887.9441,74.9998 M915.3038,49.99999999999999 L937.1884,49.99999999999999 M937.1884,49.99999999999999 C950.9,49.99999999999999,950.8384,25.000199999999992,964.5481,25.000199999999992 M937.1884,49.99999999999999 C950.9,49.99999999999999,950.8384,74.9998,964.5481,74.9998 M875.0,24.999999999999993 L888.0,24.999999999999993 M888.0019,74.9998 L875.0,74.9998 M962.6453,74.9998 L975.0,74.9998 M962.1944,24.999799999999993 L975.0,24.999799999999993\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"925\" y=\"38\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M947,53 L957,53 L957,63 L947,63 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"952\" y=\"60\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M975,25 L995,25 M1005,25 L1025,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M990,35 L1010,35 L1010,15 L990,15 L990,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1000\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M1025,25 L1045,25 M1055,25 L1075,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1040,35 L1060,35 L1060,15 L1040,15 L1040,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1050\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M975,75 L995,75 M1005,75 L1025,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M990,85 L1010,85 L1010,65 L990,65 L990,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1000\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M1025,75.0 L1075,75.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1077,102 L1423,102 L1423,198 L1077,198 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1079\" y=\"205\" font-size=\"8\" text-anchor=\"start\">H</text>\n",
       "<path d=\"M1087.9442,125.0002 C1101.6537999999998,125.0002,1101.5922999999998,150.0,1115.3019,150.0 M1115.3038,150.0 C1101.5921999999998,150.0,1101.6537999999998,174.9998,1087.9441,174.9998 M1115.3038,150.0 L1137.1884,150.0 M1137.1884,150.0 C1150.9,150.0,1150.8384,125.0002,1164.5481,125.0002 M1137.1884,150.0 C1150.9,150.0,1150.8384,174.9998,1164.5481,174.9998 M1075.0,125.0 L1088.0,125.0 M1088.0019,174.9998 L1075.0,174.9998 M1162.6453,174.9998 L1175.0,174.9998 M1162.1944,124.9998 L1175.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"1125\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M1147,153 L1157,153 L1157,163 L1147,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1152\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M1175,125 L1195,125 M1205,125 L1225,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1190,135 L1210,135 L1210,115 L1190,115 L1190,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1200\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M1175,175.0 L1225,175.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1237.9442,125.0002 C1251.6537999999998,125.0002,1251.5922999999998,150.0,1265.3019,150.0 M1265.3038,150.0 C1251.5921999999998,150.0,1251.6537999999998,174.9998,1237.9441,174.9998 M1265.3038,150.0 L1287.1884,150.0 M1287.1884,150.0 C1300.9,150.0,1300.8384,125.0002,1314.5481,125.0002 M1287.1884,150.0 C1300.9,150.0,1300.8384,174.9998,1314.5481,174.9998 M1225.0,125.0 L1238.0,125.0 M1238.0019,174.9998 L1225.0,174.9998 M1312.6453,174.9998 L1325.0,174.9998 M1312.1944,124.9998 L1325.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"1275\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M1297,153 L1307,153 L1307,163 L1297,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1302\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M1325,125 L1345,125 M1355,125 L1375,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1340,135 L1360,135 L1360,115 L1340,115 L1340,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1350\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M1375,125 L1395,125 M1405,125 L1425,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1390,135 L1410,135 L1410,115 L1390,115 L1390,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1400\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M1325,175 L1345,175 M1355,175 L1375,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1340,185 L1360,185 L1360,165 L1340,165 L1340,185\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1350\" y=\"194\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M1375,175.0 L1425,175.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1427,52 L1773,52 L1773,148 L1427,148 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1429\" y=\"155\" font-size=\"8\" text-anchor=\"start\">U_REF</text>\n",
       "<path d=\"M1075,75.0 L1425,75.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1437.9442,75.0002 C1451.6537999999998,75.0002,1451.5922999999998,100.0,1465.3019,100.0 M1465.3038,100.0 C1451.5921999999998,100.0,1451.6537999999998,124.9998,1437.9441,124.9998 M1465.3038,100.0 L1487.1884,100.0 M1487.1884,100.0 C1500.9,100.0,1500.8384,75.0002,1514.5481,75.0002 M1487.1884,100.0 C1500.9,100.0,1500.8384,124.9998,1514.5481,124.9998 M1425.0,75.0 L1438.0,75.0 M1438.0019,124.9998 L1425.0,124.9998 M1512.6453,124.9998 L1525.0,124.9998 M1512.1944,74.9998 L1525.0,74.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"1475\" y=\"88\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M1497,103 L1507,103 L1507,113 L1497,113 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1502\" y=\"110\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M1525,75 L1545,75 M1555,75 L1575,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1540,85 L1560,85 L1560,65 L1540,65 L1540,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1550\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=pi</text>\n",
       "<path d=\"M1525,125.0 L1575,125.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1587.9442,75.0002 C1601.6537999999998,75.0002,1601.5922999999998,100.0,1615.3019,100.0 M1615.3038,100.0 C1601.5921999999998,100.0,1601.6537999999998,124.9998,1587.9441,124.9998 M1615.3038,100.0 L1637.1884,100.0 M1637.1884,100.0 C1650.9,100.0,1650.8384,75.0002,1664.5481,75.0002 M1637.1884,100.0 C1650.9,100.0,1650.8384,124.9998,1664.5481,124.9998 M1575.0,75.0 L1588.0,75.0 M1588.0019,124.9998 L1575.0,124.9998 M1662.6453,124.9998 L1675.0,124.9998 M1662.1944,74.9998 L1675.0,74.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"1625\" y=\"88\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M1647,103 L1657,103 L1657,113 L1647,113 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1652\" y=\"110\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M1675,75 L1695,75 M1705,75 L1725,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1690,85 L1710,85 L1710,65 L1690,65 L1690,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1700\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M1725,75 L1745,75 M1755,75 L1775,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1740,85 L1760,85 L1760,65 L1740,65 L1740,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1750\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M1675,125 L1695,125 M1705,125 L1725,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1690,135 L1710,135 L1710,115 L1690,115 L1690,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1700\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M1075,25.0 L1775,25.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1725,125.0 L1775,125.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1777,102 L2123,102 L2123,198 L1777,198 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1779\" y=\"205\" font-size=\"8\" text-anchor=\"start\">U_E</text>\n",
       "<path d=\"M1425,175.0 L1775,175.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1787.9442,125.0002 C1801.6537999999998,125.0002,1801.5922999999998,150.0,1815.3019,150.0 M1815.3038,150.0 C1801.5921999999998,150.0,1801.6537999999998,174.9998,1787.9441,174.9998 M1815.3038,150.0 L1837.1884,150.0 M1837.1884,150.0 C1850.9,150.0,1850.8384,125.0002,1864.5481,125.0002 M1837.1884,150.0 C1850.9,150.0,1850.8384,174.9998,1864.5481,174.9998 M1775.0,125.0 L1788.0,125.0 M1788.0019,174.9998 L1775.0,174.9998 M1862.6453,174.9998 L1875.0,174.9998 M1862.1944,124.9998 L1875.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"1825\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M1847,153 L1857,153 L1857,163 L1847,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1852\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M1875,125 L1895,125 M1905,125 L1925,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1890,135 L1910,135 L1910,115 L1890,115 L1890,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1900\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=2*pi</text>\n",
       "<path d=\"M1875,175.0 L1925,175.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1937.9442,125.0002 C1951.6537999999998,125.0002,1951.5922999999998,150.0,1965.3019,150.0 M1965.3038,150.0 C1951.5921999999998,150.0,1951.6537999999998,174.9998,1937.9441,174.9998 M1965.3038,150.0 L1987.1884,150.0 M1987.1884,150.0 C2000.9,150.0,2000.8384,125.0002,2014.5481,125.0002 M1987.1884,150.0 C2000.9,150.0,2000.8384,174.9998,2014.5481,174.9998 M1925.0,125.0 L1938.0,125.0 M1938.0019,174.9998 L1925.0,174.9998 M2012.6453,174.9998 L2025.0,174.9998 M2012.1944,124.9998 L2025.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"1975\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M1997,153 L2007,153 L2007,163 L1997,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"2002\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M2025,125 L2045,125 M2055,125 L2075,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M2040,135 L2060,135 L2060,115 L2040,115 L2040,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"2050\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M2075,125 L2095,125 M2105,125 L2125,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M2090,135 L2110,135 L2110,115 L2090,115 L2090,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"2100\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M2025,175 L2045,175 M2055,175 L2075,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M2040,185 L2060,185 L2060,165 L2040,165 L2040,185\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"2050\" y=\"194\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M2075,175.0 L2125,175.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1775,25.0 L2125,25.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1775,75.0 L2125,75.0\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M2125,25.0 L2140,25.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M2125,75.0 L2140,75.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M2125,125.0 L2140,125.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M2125,175.0 L2140,175.0\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"2150\" y=\"28.0\" font-size=\"6\" text-anchor=\"end\">0</text>\n",
       "<text x=\"2150\" y=\"78.0\" font-size=\"6\" text-anchor=\"end\">1</text>\n",
       "<text x=\"2150\" y=\"128.0\" font-size=\"6\" text-anchor=\"end\">2</text>\n",
       "<text x=\"2150\" y=\"178.0\" font-size=\"6\" text-anchor=\"end\">3</text>\n",
       "<text x=\"0\" y=\"28.0\" font-size=\"6\" text-anchor=\"start\">0</text>\n",
       "<text x=\"0\" y=\"78.0\" font-size=\"6\" text-anchor=\"start\">1</text>\n",
       "<text x=\"0\" y=\"128.0\" font-size=\"6\" text-anchor=\"start\">2</text>\n",
       "<text x=\"0\" y=\"178.0\" font-size=\"6\" text-anchor=\"start\">3</text>\n",
       "</svg>"
      ],
      "text/plain": [
       "<drawsvg.drawing.Drawing at 0x7fb64baf0340>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quantum_circuit = pcvl.Circuit(4)\n",
    "quantum_circuit.add(1, state_prep).add(0, hadamard).add(2, hadamard).add(2, env).add(0, hadamard).add(2, hadamard).add(1, ref) #circuit for quantum strategy\n",
    "quantum_circuit.add(2,env) #appending directly the classical round (without preparation) at the end\n",
    "pcvl.pdisplay(quantum_circuit, recursive=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "367229cf",
   "metadata": {},
   "source": [
    "### Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "318570c5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Simulation parameters\n",
    "N_AGENTS = 100 #number of agents that we simulate and average over\n",
    "N_EPOCH = 1000\n",
    "H_0 = 99\n",
    "H_1 = 1\n",
    "EPS0 = H_1 / (H_0+H_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46ff0d04",
   "metadata": {},
   "source": [
    "#### Reward function\n",
    "First we define a reward function that takes as an input a circuit, output a sample state and returns True if it corresponds to a rewarded state (False otherwise)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "2369c08f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_reward(circuit: pcvl.Circuit) -> bool:\n",
    "    proc = pcvl.Processor(\"SLOS\", circuit)\n",
    "    proc.with_input(pcvl.BasicState([0, 1, 0, 0]))\n",
    "    sampler = pcvl.algorithm.Sampler(proc)\n",
    "    samples = sampler.samples(1)\n",
    "\n",
    "    # Take a random sample and check if it's the rewarded state or not\n",
    "    return samples[\"results\"][0] == pcvl.BasicState([0, 0, 0, 1])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae5b5de3",
   "metadata": {},
   "source": [
    "#### Classical strategy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2aa85433",
   "metadata": {},
   "source": [
    "Below we gather everything defined above to run the purely classical strategy from the article."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "5cdf619c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4569e50c5b80450f9a7e963aad889672",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "FloatProgress(value=0.0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eta_classical = []\n",
    "\n",
    "# Percentage bar\n",
    "f = FloatProgress(min=0, max=N_AGENTS)\n",
    "display(f)\n",
    "\n",
    "for agent in range(N_AGENTS): #Loop and average over all agents\n",
    "    f.value = agent\n",
    "    # Initialize initial score\n",
    "    h_0 = H_0\n",
    "    h_1 = H_1\n",
    "    eps = h_1 / (h_0 + h_1)\n",
    "\n",
    "    # Initialize circuit with initial probability and corresponding angles\n",
    "    xi = math.asin(eps**0.5)\n",
    "    \n",
    "    theta1 = math.pi - 2*xi\n",
    "    theta_prep.set_value(theta1)\n",
    "    theta2_prep.set_value(-math.pi/2 - theta1/2)\n",
    "\n",
    "    # Arrays of epsilon\n",
    "    eps_array = []\n",
    "    for i in range(N_EPOCH):\n",
    "        if get_reward(classical_circuit): #update policy if output state corresponds to a rewarded state\n",
    "            h_1 = h_1 + 2\n",
    "            eps = h_1 / (h_0 + h_1)\n",
    "            xi = math.asin(eps**0.5)\n",
    "            theta1 = math.pi - 2*xi\n",
    "            theta_prep.set_value(theta1)\n",
    "            theta2_prep.set_value(-math.pi/2 - theta1/2)\n",
    "            eps_array.append(1)\n",
    "        else:\n",
    "            eps_array.append(0)\n",
    "\n",
    "    eta_classical.append(eps_array)\n",
    "\n",
    "eta_classical = np.array(eta_classical)\n",
    "f.value = N_AGENTS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "413721c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.mean(eta_classical, axis=0)[::2], \".\", label=\"Fully classical strategy\")\n",
    "plt.xlabel(\"Even epochs\")\n",
    "plt.ylabel(\"$\\eta$\")\n",
    "plt.legend()\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ab3f4c9",
   "metadata": {},
   "source": [
    "Here we plot the proportion of agents that gets a reward. In the first epochs, the probability of getting a reward is small and few agents get some. However, once an agent gets a reward, they are more likely to get a reward in the future."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4e33516",
   "metadata": {},
   "source": [
    "#### Quantum strategy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3235182e",
   "metadata": {},
   "source": [
    "Below we run the purely quantum strategy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "63cdbf11",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "856d305ae94641c388ad55ae0340ed58",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "FloatProgress(value=0.0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eta_quantum = []\n",
    "\n",
    "# Percentage bar\n",
    "f = FloatProgress(min=0, max=N_AGENTS)\n",
    "display(f)\n",
    "\n",
    "for agent in range(N_AGENTS):\n",
    "    f.value = agent\n",
    "    # Initialize initial scores\n",
    "    h_0 = H_0\n",
    "    h_1 = H_1\n",
    "    eps = h_1 / (h_0 + h_1)\n",
    "\n",
    "    # Initialize circuit with initial probability\n",
    "    xi = math.asin(eps**0.5)\n",
    "    \n",
    "    theta1 = math.pi - 2*xi\n",
    "    theta_prep.set_value(theta1)\n",
    "    theta2_prep.set_value(-math.pi/2 - theta1/2)\n",
    "    \n",
    "    theta2 = math.pi - 4*xi\n",
    "    theta_ref.set_value(theta2)\n",
    "    theta2_ref.set_value(-math.pi/2 - theta2/2)\n",
    "\n",
    "    # Arrays of epsilon\n",
    "    eps_array = []\n",
    "    for i in range(N_EPOCH//2):\n",
    "        if get_reward(quantum_circuit):\n",
    "            h_1 = h_1 + 2\n",
    "            eps = h_1 / (h_0 + h_1)\n",
    "            xi = math.asin(eps**0.5)\n",
    "            \n",
    "            theta1 = math.pi - 2*xi\n",
    "            theta_prep.set_value(theta1)\n",
    "            theta2_prep.set_value(-math.pi/2 - theta1/2)\n",
    "            \n",
    "            theta2 = math.pi - 4*xi\n",
    "            theta_ref.set_value(theta2)\n",
    "            theta2_ref.set_value(-math.pi/2 - theta2/2)\n",
    "            \n",
    "            eps_array.append(0.5)\n",
    "            eps_array.append(0.5)\n",
    "        else:\n",
    "            eps_array.append(0)\n",
    "            eps_array.append(0)\n",
    "\n",
    "    eta_quantum.append(eps_array)\n",
    "\n",
    "eta_quantum = np.array(eta_quantum)\n",
    "f.value=N_AGENTS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "6678e44f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.mean(eta_quantum, axis=0)[::2], \".\", label=\"Fully quantum strategy\")\n",
    "plt.xlabel(\"Even epochs\")\n",
    "plt.ylabel(\"$\\eta$\")\n",
    "plt.legend()\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc7ac058",
   "metadata": {},
   "source": [
    "Here we see a different behavior. With Grover's amplification, getting a reward is more likely in the first epochs. However, as the probability gets updated, one of Grover's amplification feature will manifest itself: we start to \"overshoot\" or rotate too much and we get past the winning state, and once we got past it, it is not possible to recover the winning state. We converge to a state with zero probability of getting a reward and nothing will get updated. This is why we need to consider an hybrid strategy."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eee6f816",
   "metadata": {},
   "source": [
    "#### Classical-quantum strategy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfe8e73e",
   "metadata": {},
   "source": [
    "We want to start with a quantum strategy, and then switch to a classical strategy when e start to overshoot. This happens when the probability of winning in the quantum strategy gets lower than the classical one.\n",
    "\n",
    "Due to normalization (and the fact that the quantum strategy takes twice as many epochs than the classical one), this corresponds to solve the equation\n",
    "\n",
    "$$\\frac{1}{2}\\sin^2(3\\xi) = \\sin^2(\\xi)$$\n",
    "\n",
    "The solution can be found numerically and gives a value of $\\xi = 0.6811$ which corresponds to $\\varepsilon=\\sin^2(\\xi)=0.396$.\n",
    "\n",
    "We then choose $Q_L$ to be the value where we switch from quantum to classical and the only requirement is $Q_L<0.396$. To follow [1] we will choose, $Q_L = 0.37$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "90a4acc1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "638a042dc0c84626862f2892b912d2ba",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "FloatProgress(value=0.0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "QL = 0.37\n",
    "eta_classical_quantum = []\n",
    "\n",
    "# Percentage bar\n",
    "f = FloatProgress(min=0, max=N_AGENTS)\n",
    "display(f)\n",
    "\n",
    "for agent in range(N_AGENTS):\n",
    "    f.value = agent\n",
    "    # Initialize initial scores\n",
    "    h_0 = H_0\n",
    "    h_1 = H_1\n",
    "    eps = h_1 / (h_0 + h_1)\n",
    "\n",
    "    # Initialize circuit with initial probability\n",
    "    xi = math.asin(eps**0.5)\n",
    "    \n",
    "    theta1 = math.pi - 2*xi\n",
    "    theta_prep.set_value(theta1)\n",
    "    theta2_prep.set_value(-math.pi/2 - theta1/2)\n",
    "    \n",
    "    theta2 = math.pi - 4*xi\n",
    "    theta_ref.set_value(theta2)\n",
    "    theta2_ref.set_value(-math.pi/2 - theta2/2)\n",
    "\n",
    "    # Arrays of epsilon\n",
    "    eps_array = []\n",
    "    i = 0\n",
    "    while i < N_EPOCH:\n",
    "        if eps < QL:\n",
    "            # Perform a quantum round\n",
    "            if get_reward(quantum_circuit):\n",
    "                h_1 = h_1 + 2\n",
    "                eps = h_1 / (h_0 + h_1)\n",
    "                xi = math.asin(eps**0.5)\n",
    "                theta1 = math.pi - 2*xi\n",
    "                theta_prep.set_value(theta1)\n",
    "                theta2_prep.set_value(-math.pi/2 - theta1/2)\n",
    "    \n",
    "                theta2 = math.pi - 4*xi\n",
    "                theta_ref.set_value(theta2)\n",
    "                theta2_ref.set_value(-math.pi/2 - theta2/2)\n",
    "                eps_array.append(0.5)\n",
    "                eps_array.append(0.5)\n",
    "            else:\n",
    "                eps_array.append(0)\n",
    "                eps_array.append(0)\n",
    "\n",
    "            # Update epoch by 2\n",
    "            i = i + 2\n",
    "        else:\n",
    "            # Perform a classical round\n",
    "            if get_reward(classical_circuit):\n",
    "                h_1 = h_1 + 2\n",
    "                eps = h_1 / (h_0 + h_1)\n",
    "                xi = math.asin(eps**0.5)\n",
    "                theta1 = math.pi - 2*xi\n",
    "                theta_prep.set_value(theta1)\n",
    "                theta2_prep.set_value(-math.pi/2 - theta1/2)\n",
    "\n",
    "                eps_array.append(1)\n",
    "            else:\n",
    "                eps_array.append(0)\n",
    "            # Update epoch by 1\n",
    "            i = i + 1\n",
    "\n",
    "    eta_classical_quantum.append(eps_array)\n",
    "\n",
    "eta_classical_quantum = np.array(eta_classical_quantum)\n",
    "f.value=N_AGENTS"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20a92f86",
   "metadata": {},
   "source": [
    "#### Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "957d52f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.mean(eta_classical, axis=0)[::2], \".\", label=\"Fully classical strategy\")\n",
    "plt.plot(np.mean(eta_quantum, axis=0)[::2], \".\", label=\"Fully quantum strategy\")\n",
    "plt.plot(np.mean(eta_classical_quantum,axis=0,)[::2],\".\",label=\"Quantum-classical strategy\",)\n",
    "plt.xlabel(\"Even epochs\")\n",
    "plt.ylabel(\"$\\eta$\")\n",
    "plt.legend()\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4390ce7",
   "metadata": {},
   "source": [
    "## Conclusion"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "34dd02db",
   "metadata": {},
   "source": [
    "Simulating the circuits of [1], we are able to reproduce their results. Data are still noisier than the results due to a smaller number agents. A parallelized version of this code was executed with 10 000 agents and the following results were found:\n",
    "\n",
    "![results_10000.png](../_static/img/reinforcement-learning_results_10000.png)\n",
    "\n",
    "which are very close to the paper results.\n",
    "\n",
    "It's possible to play with the value of $Q_L$ and the number of agents. Remember that the simulation time is linear with the number of agents."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "911dd875",
   "metadata": {},
   "source": [
    "## Acknowledgement"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7721eae9",
   "metadata": {},
   "source": [
    "This work was initially done during the Hackathon on Linear Optical Quantum Communication (LOQCathon) organised by [Quandela](https://www.quandela.com/) and [QICS](https://qics.sorbonne-universite.fr/en) (Quantum Information Center of Sorbonne Université), by the team composed of Luís Bugalho, Laura dos Santos Martins, Paolo Fittipaldi, Yoann Piétri and Verena Yacoub. The supervision was provided by Pierre-Emmanuel Emeriau."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "441c442e",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    ">  [1] V. Saggio, B. E. Asenbeck, A.  Hamann, et al. Experimental quantum speed-up in reinforcement learning agents. [Nature](https://doi.org/10.1038/s41586-021-03242-7), 591(7849), 229-233 (2021).\n",
    "\n",
    " > [2] A. Hamann, S. Wölk. Performance analysis of a hybrid agent for quantum-accessible reinforcement learning. [New Journal of Physics](https://doi.org/10.1088/1367-2630/ac5b56 ), 24(3), 033044 (2022)."
   ]
  }
 ],
 "metadata": {
  "language_info": {
   "name": "python"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}