{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f1aad8daa8cdd20",
   "metadata": {},
   "source": [
    "# Theory validation experiment: Expressive power of the variational linear quantum photonic circuit (dependent of photon number)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6f644861594f155",
   "metadata": {},
   "source": [
    "The goal here will be to fit a degree 3 Fourier series g(x) with a Variational Quantum Circuit (VQC) using MerLin for the optimization. Since this is a fitting task, we won't use a validation or test dataset because our goal is to overfit on the data to assess the expressivity of a VQC.\n",
    "\n",
    "As we will see, the expressivity of a VQC depends on the number of photons sent through the quantum circuit.\n",
    "\n",
    "This notebook presents an experiment from the paper: [Fock State-enhanced Expressivity of Quantum Machine Learning Models](https://arxiv.org/abs/2107.05224)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ecce09be4899e558",
   "metadata": {},
   "source": [
    "## 0. Imports and prep"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "acbe33cef30ce280",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-10T08:59:00.364706500Z",
     "start_time": "2025-11-10T08:59:00.110778Z"
    }
   },
   "outputs": [],
   "source": [
    "# Import required libraries\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import perceval as pcvl\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from tqdm import tqdm\n",
    "\n",
    "from merlin import QuantumLayer"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6f7fa599036c74f",
   "metadata": {},
   "source": [
    "## 1. Define input domain, x, and target function g(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f7025aef462f8b54",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-10T08:59:00.395762900Z",
     "start_time": "2025-11-10T08:59:00.330803400Z"
    }
   },
   "outputs": [],
   "source": [
    "x = np.arange(-3 * np.pi, 3 * np.pi + 0.01, 0.05)\n",
    "\n",
    "# Fourier coefficents\n",
    "c_0 = 0.2\n",
    "c_1 = 0.69 + 0.52j\n",
    "c_2 = 0.81 + 0.41j\n",
    "c_3 = 0.68 + 0.82j\n",
    "# We want real valued g(x) so we have c_{-n} = conjugate( c_{n})\n",
    "coefs = np.array([np.conj(c_3), np.conj(c_2), np.conj(c_1), c_0, c_1, c_2, c_3])\n",
    "n = np.arange(-3, 4, 1)\n",
    "\n",
    "# Compute the Fourier series sum\n",
    "g = np.zeros_like(x, dtype=complex)\n",
    "for k, c in zip(n, coefs, strict=False):\n",
    "    g += c * np.exp(1j * k * x)\n",
    "\n",
    "# g should be real valued\n",
    "assert np.allclose(g, g.real), \"g != g.real\"\n",
    "g = g.real"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a7326c63d78217e",
   "metadata": {},
   "source": [
    " Let's visualize g(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "3f27964b6712204d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-10T08:59:02.329037500Z",
     "start_time": "2025-11-10T08:59:00.330803400Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 800x400 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 0 Axes>"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot using matplotlib\n",
    "plt.figure(figsize=(8, 4))\n",
    "plt.scatter(x, g, label=\"g(x)\", s=30)\n",
    "plt.title(\"Visualization of g(x) from Fourier Series\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"g(x)\")\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "plt.clf()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9fb78e24366119bb",
   "metadata": {},
   "source": [
    "## 2. Model definitions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d141b4d4717e128",
   "metadata": {},
   "source": [
    "First off, we define the photonic circuit using Perceval."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "f65611c13781e51c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-10T08:59:02.397888200Z",
     "start_time": "2025-11-10T08:59:01.487951800Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "<drawsvg.drawing.Drawing at 0x1856d4a3950>",
      "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=\"2445.0\" height=\"218.75\" viewBox=\"-28.0 0 1956.0 175.0\">\n<defs>\n</defs>\n<path d=\"M10,25.0 L25,25.0\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M10,75.0 L25,75.0\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M10,125.0 L25,125.0\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M25,25 L53,25 L72,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M78,44 L97,25 L125,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M25,75 L53,75 L72,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M78,56 L97,75 L125,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M50,43 L100,43 L100,57 L50,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"75\" y=\"85\" font-size=\"7\" text-anchor=\"middle\"></text>\n<text x=\"75\" y=\"26\" font-size=\"7\" text-anchor=\"middle\"></text>\n<path d=\"M50,43 L100,43 L100,47 L50,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M93,50 L103,50 L103,60 L93,60 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"98\" y=\"57\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n<path d=\"M125,25 L175,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M130,40 L139,40 L153,10 L144,10 L130,40 L139,40 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"147\" y=\"38\" font-size=\"7\" text-anchor=\"start\">Φ=theta_li0_ps</text>\n<path d=\"M125,75.0 L175,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M175,25 L203,25 L222,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M228,44 L247,25 L275,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M175,75 L203,75 L222,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M228,56 L247,75 L275,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M200,43 L250,43 L250,57 L200,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"225\" y=\"85\" font-size=\"7\" text-anchor=\"middle\"></text>\n<text x=\"225\" y=\"26\" font-size=\"7\" text-anchor=\"middle\"></text>\n<path d=\"M200,43 L250,43 L250,47 L200,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M243,50 L253,50 L253,60 L243,60 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"248\" y=\"57\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n<path d=\"M275,25 L325,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M280,40 L289,40 L303,10 L294,10 L280,40 L289,40 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"297\" y=\"38\" font-size=\"7\" text-anchor=\"start\">Φ=theta_lo0_ps</text>\n<path d=\"M275,75.0 L325,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M25,125.0 L325,125.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M325,75 L353,75 L372,94\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M378,94 L397,75 L425,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M325,125 L353,125 L372,106\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M378,106 L397,125 L425,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M350,93 L400,93 L400,107 L350,107 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"375\" y=\"135\" font-size=\"7\" text-anchor=\"middle\"></text>\n<text x=\"375\" y=\"76\" font-size=\"7\" text-anchor=\"middle\"></text>\n<path d=\"M350,93 L400,93 L400,97 L350,97 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M393,100 L403,100 L403,110 L393,110 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"398\" y=\"107\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n<path d=\"M425,75 L475,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M430,90 L439,90 L453,60 L444,60 L430,90 L439,90 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"447\" y=\"88\" font-size=\"7\" text-anchor=\"start\">Φ=theta_li1_ps</text>\n<path d=\"M425,125.0 L475,125.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M475,75 L503,75 L522,94\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M528,94 L547,75 L575,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M475,125 L503,125 L522,106\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M528,106 L547,125 L575,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M500,93 L550,93 L550,107 L500,107 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"525\" y=\"135\" font-size=\"7\" text-anchor=\"middle\"></text>\n<text x=\"525\" y=\"76\" font-size=\"7\" text-anchor=\"middle\"></text>\n<path d=\"M500,93 L550,93 L550,97 L500,97 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M543,100 L553,100 L553,110 L543,110 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"548\" y=\"107\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n<path d=\"M575,75 L625,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M580,90 L589,90 L603,60 L594,60 L580,90 L589,90 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"597\" y=\"88\" font-size=\"7\" text-anchor=\"start\">Φ=theta_lo1_ps</text>\n<path d=\"M325,25.0 L625,25.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M575,125.0 L625,125.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M625,25 L653,25 L672,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M678,44 L697,25 L725,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M625,75 L653,75 L672,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M678,56 L697,75 L725,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M650,43 L700,43 L700,57 L650,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"675\" y=\"85\" font-size=\"7\" text-anchor=\"middle\"></text>\n<text x=\"675\" y=\"26\" font-size=\"7\" text-anchor=\"middle\"></text>\n<path d=\"M650,43 L700,43 L700,47 L650,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M693,50 L703,50 L703,60 L693,60 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"698\" y=\"57\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n<path d=\"M725,25 L775,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M730,40 L739,40 L753,10 L744,10 L730,40 L739,40 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"747\" y=\"38\" font-size=\"7\" text-anchor=\"start\">Φ=theta_li2_ps</text>\n<path d=\"M725,75.0 L775,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M775,25 L803,25 L822,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M828,44 L847,25 L875,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M775,75 L803,75 L822,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M828,56 L847,75 L875,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M800,43 L850,43 L850,57 L800,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"825\" y=\"85\" font-size=\"7\" text-anchor=\"middle\"></text>\n<text x=\"825\" y=\"26\" font-size=\"7\" text-anchor=\"middle\"></text>\n<path d=\"M800,43 L850,43 L850,47 L800,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M843,50 L853,50 L853,60 L843,60 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"848\" y=\"57\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n<path d=\"M875,25 L925,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M880,40 L889,40 L903,10 L894,10 L880,40 L889,40 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"897\" y=\"38\" font-size=\"7\" text-anchor=\"start\">Φ=theta_lo2_ps</text>\n<path d=\"M875,75.0 L925,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M625,125.0 L925,125.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M925,75 L975,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M930,90 L939,90 L953,60 L944,60 L930,90 L939,90 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"947\" y=\"88\" font-size=\"7\" text-anchor=\"start\">Φ=px1</text>\n<path d=\"M925,25.0 L975,25.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M975,25 L1003,25 L1022,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1028,44 L1047,25 L1075,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M975,75 L1003,75 L1022,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1028,56 L1047,75 L1075,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1000,43 L1050,43 L1050,57 L1000,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1025\" y=\"85\" font-size=\"7\" text-anchor=\"middle\"></text>\n<text x=\"1025\" y=\"26\" font-size=\"7\" text-anchor=\"middle\"></text>\n<path d=\"M1000,43 L1050,43 L1050,47 L1000,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1043,50 L1053,50 L1053,60 L1043,60 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1048\" y=\"57\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n<path d=\"M1075,25 L1125,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1080,40 L1089,40 L1103,10 L1094,10 L1080,40 L1089,40 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1097\" y=\"38\" font-size=\"7\" text-anchor=\"start\">Φ=theta_ri0_ps</text>\n<path d=\"M1075,75.0 L1125,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1125,25 L1153,25 L1172,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1178,44 L1197,25 L1225,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1125,75 L1153,75 L1172,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1178,56 L1197,75 L1225,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1150,43 L1200,43 L1200,57 L1150,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1175\" y=\"85\" font-size=\"7\" text-anchor=\"middle\"></text>\n<text x=\"1175\" y=\"26\" font-size=\"7\" text-anchor=\"middle\"></text>\n<path d=\"M1150,43 L1200,43 L1200,47 L1150,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1193,50 L1203,50 L1203,60 L1193,60 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1198\" y=\"57\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n<path d=\"M1225,25 L1275,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1230,40 L1239,40 L1253,10 L1244,10 L1230,40 L1239,40 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1247\" y=\"38\" font-size=\"7\" text-anchor=\"start\">Φ=theta_ro0_ps</text>\n<path d=\"M1225,75.0 L1275,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M925,125.0 L1275,125.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1275,75 L1303,75 L1322,94\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1328,94 L1347,75 L1375,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1275,125 L1303,125 L1322,106\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1328,106 L1347,125 L1375,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1300,93 L1350,93 L1350,107 L1300,107 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1325\" y=\"135\" font-size=\"7\" text-anchor=\"middle\"></text>\n<text x=\"1325\" y=\"76\" font-size=\"7\" text-anchor=\"middle\"></text>\n<path d=\"M1300,93 L1350,93 L1350,97 L1300,97 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1343,100 L1353,100 L1353,110 L1343,110 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1348\" y=\"107\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n<path d=\"M1375,75 L1425,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1380,90 L1389,90 L1403,60 L1394,60 L1380,90 L1389,90 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1397\" y=\"88\" font-size=\"7\" text-anchor=\"start\">Φ=theta_ri1_ps</text>\n<path d=\"M1375,125.0 L1425,125.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1425,75 L1453,75 L1472,94\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1478,94 L1497,75 L1525,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1425,125 L1453,125 L1472,106\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1478,106 L1497,125 L1525,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1450,93 L1500,93 L1500,107 L1450,107 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1475\" y=\"135\" font-size=\"7\" text-anchor=\"middle\"></text>\n<text x=\"1475\" y=\"76\" font-size=\"7\" text-anchor=\"middle\"></text>\n<path d=\"M1450,93 L1500,93 L1500,97 L1450,97 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1493,100 L1503,100 L1503,110 L1493,110 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1498\" y=\"107\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n<path d=\"M1525,75 L1575,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1530,90 L1539,90 L1553,60 L1544,60 L1530,90 L1539,90 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1547\" y=\"88\" font-size=\"7\" text-anchor=\"start\">Φ=theta_ro1_ps</text>\n<path d=\"M1275,25.0 L1575,25.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1525,125.0 L1575,125.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1575,25 L1603,25 L1622,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1628,44 L1647,25 L1675,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1575,75 L1603,75 L1622,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1628,56 L1647,75 L1675,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1600,43 L1650,43 L1650,57 L1600,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1625\" y=\"85\" font-size=\"7\" text-anchor=\"middle\"></text>\n<text x=\"1625\" y=\"26\" font-size=\"7\" text-anchor=\"middle\"></text>\n<path d=\"M1600,43 L1650,43 L1650,47 L1600,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1643,50 L1653,50 L1653,60 L1643,60 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1648\" y=\"57\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n<path d=\"M1675,25 L1725,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1680,40 L1689,40 L1703,10 L1694,10 L1680,40 L1689,40 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1697\" y=\"38\" font-size=\"7\" text-anchor=\"start\">Φ=theta_ri2_ps</text>\n<path d=\"M1675,75.0 L1725,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1725,25 L1753,25 L1772,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1778,44 L1797,25 L1825,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1725,75 L1753,75 L1772,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1778,56 L1797,75 L1825,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1750,43 L1800,43 L1800,57 L1750,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n<text x=\"1775\" y=\"85\" font-size=\"7\" text-anchor=\"middle\"></text>\n<text x=\"1775\" y=\"26\" font-size=\"7\" text-anchor=\"middle\"></text>\n<path d=\"M1750,43 L1800,43 L1800,47 L1750,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n<path d=\"M1793,50 L1803,50 L1803,60 L1793,60 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n<text x=\"1798\" y=\"57\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n<path d=\"M1825,25 L1875,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1830,40 L1839,40 L1853,10 L1844,10 L1830,40 L1839,40 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n<text x=\"1847\" y=\"38\" font-size=\"7\" text-anchor=\"start\">Φ=theta_ro2_ps</text>\n<path d=\"M1825,75.0 L1875,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1575,125.0 L1875,125.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n<path d=\"M1875,25.0 L1890,25.0\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M1875,75.0 L1890,75.0\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<path d=\"M1875,125.0 L1890,125.0\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n<text x=\"1900\" y=\"28.0\" font-size=\"6\" text-anchor=\"end\">0</text>\n<text x=\"1900\" y=\"78.0\" font-size=\"6\" text-anchor=\"end\">1</text>\n<text x=\"1900\" y=\"128.0\" font-size=\"6\" text-anchor=\"end\">2</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</svg>"
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def create_vqc_general(m, input_size):\n",
    "    \"\"\"\n",
    "    Create variational quantum classifier with specified number of modes using general meshes.\n",
    "\n",
    "    Args:\n",
    "        m (int): Number of modes in the photonic circuit\n",
    "        input_size (int): Number of input features to encode\n",
    "\n",
    "    Returns:\n",
    "        pcvl.Circuit: The constructed quantum circuit\n",
    "    \"\"\"\n",
    "    wl = pcvl.GenericInterferometer(\n",
    "        m,\n",
    "        lambda i: pcvl.BS()\n",
    "        // pcvl.PS(pcvl.P(f\"theta_li{i}_ps\"))\n",
    "        // pcvl.BS()\n",
    "        // pcvl.PS(pcvl.P(f\"theta_lo{i}_ps\")),\n",
    "        shape=pcvl.InterferometerShape.RECTANGLE,\n",
    "    )\n",
    "\n",
    "    c_var = pcvl.Circuit(m)\n",
    "    for i in range(input_size):\n",
    "        px = pcvl.P(f\"px{i + 1}\")\n",
    "        c_var.add(i + (m - input_size) // 2, pcvl.PS(px))\n",
    "\n",
    "    wr = pcvl.GenericInterferometer(\n",
    "        m,\n",
    "        lambda i: pcvl.BS()\n",
    "        // pcvl.PS(pcvl.P(f\"theta_ri{i}_ps\"))\n",
    "        // pcvl.BS()\n",
    "        // pcvl.PS(pcvl.P(f\"theta_ro{i}_ps\")),\n",
    "        shape=pcvl.InterferometerShape.RECTANGLE,\n",
    "    )\n",
    "\n",
    "    c = pcvl.Circuit(m)\n",
    "    c.add(0, wl, merge=True)\n",
    "    c.add(0, c_var, merge=True)\n",
    "    c.add(0, wr, merge=True)\n",
    "\n",
    "    return c\n",
    "\n",
    "\n",
    "def count_parameters(model):\n",
    "    \"\"\"\n",
    "    Count trainable parameters in a PyTorch model.\n",
    "\n",
    "    Args:\n",
    "        model (nn.Module): PyTorch model to analyze\n",
    "\n",
    "    Returns:\n",
    "        int: Number of trainable parameters\n",
    "    \"\"\"\n",
    "    return sum(p.numel() for p in model.parameters() if p.requires_grad)\n",
    "\n",
    "\n",
    "example_circuit = create_vqc_general(3, 1)\n",
    "pcvl.pdisplay(example_circuit)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2b038907651a441",
   "metadata": {},
   "source": [
    "We will define a scaling layer for the first layer of our model. It simply multiplies the input by a constant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c50bc1ebbcf5315d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-10T08:59:02.419060900Z",
     "start_time": "2025-11-10T08:59:01.701853800Z"
    }
   },
   "outputs": [],
   "source": [
    "class ScaleLayer(nn.Module):\n",
    "    \"\"\"\n",
    "    Multiply the input tensor by a learned or fixed factor.\n",
    "\n",
    "    Args:\n",
    "        dim (int): Dimension of the input data to be encoded\n",
    "        scale_type (str): Type of scaling method. Options:\n",
    "            - \"learned\": Learnable parameter initialized randomly\n",
    "            - \"2pi\", \"/2pi\", \"pi\", \"/pi\", \"2\", \"/2\", \"1\": Fixed scaling factors\n",
    "            - \"/3pi\": Scale by 1/(3π)\n",
    "\n",
    "    Returns:\n",
    "        nn.Module that multiplies the input tensor by a scaling factor\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, dim, scale_type=\"learned\"):\n",
    "        super().__init__()\n",
    "\n",
    "        if scale_type == \"learned\":\n",
    "            self.scale = nn.Parameter(torch.rand(dim))\n",
    "        elif scale_type == \"2pi\":\n",
    "            self.scale = torch.full((dim,), 2 * torch.pi)\n",
    "        elif scale_type == \"/2pi\":\n",
    "            self.scale = torch.full((dim,), 1 / (2 * torch.pi))\n",
    "        elif scale_type == \"/2\":\n",
    "            self.scale = torch.full((dim,), 1 / 2)\n",
    "        elif scale_type == \"2\":\n",
    "            self.scale = torch.full((dim,), 2.0)\n",
    "        elif scale_type == \"pi\":\n",
    "            self.scale = torch.full((dim,), torch.pi)\n",
    "        elif scale_type == \"/pi\":\n",
    "            self.scale = torch.full((dim,), 1 / torch.pi)\n",
    "        elif scale_type == \"1\":\n",
    "            self.scale = torch.full((dim,), 1)\n",
    "        elif scale_type == \"/3pi\":\n",
    "            self.scale = torch.full((dim,), 1 / (3 * torch.pi))\n",
    "\n",
    "    def forward(self, x):\n",
    "        \"\"\"Apply scaling to input tensor.\"\"\"\n",
    "        return x * self.scale"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c877235bfbdbd7e3",
   "metadata": {},
   "source": [
    "Then, we use MerLin's QuantumLayer which allows backpropagation for optimization with gradient descent. It was also designed to be used with PyTorch so this facilitates its usage immensely.\n",
    "\n",
    "Let's create three quantum layers that each have a different input state to their circuit. Then, let's see how this affects their number of parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "e26489afd2c62593",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-10T08:59:02.447382Z",
     "start_time": "2025-11-10T08:59:01.718172700Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "VQC_[1, 0, 0]: 16 parameters\n",
      "VQC_[1, 1, 0]: 19 parameters\n",
      "VQC_[1, 1, 1]: 23 parameters\n"
     ]
    }
   ],
   "source": [
    "def create_quantum_layer(initial_state):\n",
    "    \"\"\"\n",
    "    Create a quantum layer consisting of a VQC for a specific initial state.\n",
    "\n",
    "    Args:\n",
    "        initial_state (list): The initial Fock state (e.g., [1, 0, 0] for single photon)\n",
    "\n",
    "    Returns:\n",
    "        QuantumLayer: Configured quantum layer for the given initial state\n",
    "    \"\"\"\n",
    "    vqc = QuantumLayer(\n",
    "        input_size=1,\n",
    "        circuit=create_vqc_general(3, 1),\n",
    "        trainable_parameters=[\"theta\"],\n",
    "        input_parameters=[\"px\"],\n",
    "        input_state=initial_state,\n",
    "        no_bunching=False,\n",
    "    )\n",
    "\n",
    "    return vqc\n",
    "\n",
    "\n",
    "def create_model(initial_state):\n",
    "    \"\"\"\n",
    "    Create a complete model with scaling layer and quantum layer.\n",
    "\n",
    "    Args:\n",
    "        initial_state (list): The initial Fock state for the quantum layer\n",
    "\n",
    "    Returns:\n",
    "        nn.Sequential: Complete model pipeline\n",
    "    \"\"\"\n",
    "    scale_layer = ScaleLayer(1, scale_type=\"1\")\n",
    "    vqc = create_quantum_layer(initial_state)\n",
    "    return nn.Sequential(scale_layer, vqc, nn.Linear(vqc.output_size, 1))\n",
    "\n",
    "\n",
    "# Create models with different photon numbers\n",
    "vqc_100 = create_model([1, 0, 0])  # Single photon\n",
    "vqc_110 = create_model([1, 1, 0])  # Two photons\n",
    "vqc_111 = create_model([1, 1, 1])  # Three photons\n",
    "\n",
    "models = {\"VQC_[1, 0, 0]\": vqc_100, \"VQC_[1, 1, 0]\": vqc_110, \"VQC_[1, 1, 1]\": vqc_111}\n",
    "\n",
    "# Display parameter counts\n",
    "for name, model in models.items():\n",
    "    print(f\"{name}: {count_parameters(model)} parameters\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9382c7aeed4bd962",
   "metadata": {},
   "source": [
    "## 3. Training function"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "415923bf7518fdfd",
   "metadata": {},
   "source": [
    "The optimization for the quantum model is as easy as for a classical PyTorch model thanks to MerLin. The structure of the training loop remains the same !\n",
    "\n",
    "Note that the loss function used for training is the Mean Squared Error (MSE) loss which is useful for regression tasks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "d2a16c0f40e63fcb",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-10T08:59:02.448544900Z",
     "start_time": "2025-11-10T08:59:01.964182800Z"
    }
   },
   "outputs": [],
   "source": [
    "def train_model(\n",
    "    model,\n",
    "    x_train,\n",
    "    y_train,\n",
    "    model_name,\n",
    "    n_epochs=120,\n",
    "    batch_size=32,\n",
    "    lr=0.02,\n",
    "    betas=None,\n",
    "):\n",
    "    \"\"\"\n",
    "    Train a model and return training metrics.\n",
    "\n",
    "    Args:\n",
    "        model (nn.Module): The model to train\n",
    "        x_train (torch.Tensor): Training input data\n",
    "        y_train (torch.Tensor): Training target data\n",
    "        model_name (str): Name of the model for logging\n",
    "        n_epochs (int): Number of training epochs\n",
    "        batch_size (int): Batch size for training\n",
    "        lr (float): Learning rate\n",
    "        betas (list): Beta parameters for Adam optimizer\n",
    "\n",
    "    Returns:\n",
    "        dict: Training metrics including losses and MSE values\n",
    "    \"\"\"\n",
    "    if betas is None:\n",
    "        betas = [0.9, 0.999]\n",
    "    optimizer = torch.optim.Adam(model.parameters(), lr=lr, betas=betas)\n",
    "    criterion = nn.MSELoss()\n",
    "\n",
    "    losses = []\n",
    "    train_mses = []\n",
    "\n",
    "    model.train()\n",
    "\n",
    "    pbar = tqdm(range(n_epochs), desc=f\"Training {model_name}\")\n",
    "    for _epoch in pbar:\n",
    "        permutation = torch.randperm(x_train.size()[0])\n",
    "        total_loss = 0\n",
    "\n",
    "        for i in range(0, x_train.size()[0], batch_size):\n",
    "            indices = permutation[i : i + batch_size]\n",
    "            batch_x, batch_y = x_train[indices], y_train[indices]\n",
    "\n",
    "            outputs = model(batch_x)\n",
    "            loss = criterion(outputs.squeeze(), batch_y.squeeze())\n",
    "\n",
    "            optimizer.zero_grad()\n",
    "            loss.backward()\n",
    "            optimizer.step()\n",
    "\n",
    "            total_loss += loss.item()\n",
    "\n",
    "        avg_loss = total_loss / (x_train.size()[0] // batch_size)\n",
    "        losses.append(avg_loss)\n",
    "\n",
    "        # Evaluation\n",
    "        model.eval()\n",
    "        with torch.no_grad():\n",
    "            train_outputs = model(x_train)\n",
    "            train_mse = mean_squared_error(y_train.numpy(), train_outputs)\n",
    "            train_mses.append(train_mse)\n",
    "\n",
    "            pbar.set_description(\n",
    "                f\"Training {model_name} - Loss: {avg_loss:.4f}, Train MSE: {train_mse:.4f}\"\n",
    "            )\n",
    "\n",
    "        model.train()\n",
    "\n",
    "    return {\n",
    "        \"losses\": losses,\n",
    "        \"train_mses\": train_mses,\n",
    "    }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "4b56f0bd66e6daad",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-10T09:03:48.275180900Z",
     "start_time": "2025-11-10T08:59:02.061026300Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Training VQC with initial state: [1, 0, 0] (3 runs):\n",
      "  Run 1/3...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Training VQC_[1, 0, 0]-run1 - Loss: 4.2463, Train MSE: 3.9082: 100%|██████████| 120/120 [00:33<00:00,  3.58it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Run 2/3...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Training VQC_[1, 0, 0]-run2 - Loss: 4.2884, Train MSE: 3.9146: 100%|██████████| 120/120 [00:47<00:00,  2.55it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Run 3/3...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Training VQC_[1, 0, 0]-run3 - Loss: 4.2956, Train MSE: 3.9120: 100%|██████████| 120/120 [00:47<00:00,  2.54it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Training VQC with initial state: [1, 1, 0] (3 runs):\n",
      "  Run 1/3...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Training VQC_[1, 1, 0]-run1 - Loss: 2.5241, Train MSE: 2.2689: 100%|██████████| 120/120 [00:37<00:00,  3.18it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Run 2/3...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Training VQC_[1, 1, 0]-run2 - Loss: 2.5125, Train MSE: 2.2708: 100%|██████████| 120/120 [00:38<00:00,  3.11it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Run 3/3...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Training VQC_[1, 1, 0]-run3 - Loss: 2.5023, Train MSE: 2.2807: 100%|██████████| 120/120 [00:15<00:00,  7.53it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Training VQC with initial state: [1, 1, 1] (3 runs):\n",
      "  Run 1/3...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Training VQC_[1, 1, 1]-run1 - Loss: 0.0438, Train MSE: 0.0374: 100%|██████████| 120/120 [00:22<00:00,  5.25it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Run 2/3...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Training VQC_[1, 1, 1]-run2 - Loss: 0.0000, Train MSE: 0.0000: 100%|██████████| 120/120 [00:25<00:00,  4.79it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Run 3/3...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Training VQC_[1, 1, 1]-run3 - Loss: 0.0000, Train MSE: 0.0000: 100%|██████████| 120/120 [00:17<00:00,  6.95it/s]\n"
     ]
    }
   ],
   "source": [
    "def train_models_multiple_runs(initial_states, colors, x_train, y_train, num_runs=5):\n",
    "    \"\"\"\n",
    "    Train all models multiple times and return results.\n",
    "\n",
    "    Args:\n",
    "        initial_states (list): List of initial Fock states to test\n",
    "        colors (list): List of colors for plotting\n",
    "        x_train (np.array): Training input data\n",
    "        y_train (np.array): Training target data\n",
    "        num_runs (int): Number of training runs per model\n",
    "\n",
    "    Returns:\n",
    "        tuple: (results_dict, best_models_list) containing training results and best models\n",
    "    \"\"\"\n",
    "    results = {}\n",
    "    models = []\n",
    "\n",
    "    for initial_state, color in zip(initial_states, colors, strict=False):\n",
    "        print(f\"\\nTraining VQC with initial state: {initial_state} ({num_runs} runs):\")\n",
    "        pending_models = []\n",
    "        model_runs = []\n",
    "\n",
    "        for run in range(num_runs):\n",
    "            # Create a fresh instance of the model for each run\n",
    "            vqc = create_model(initial_state)\n",
    "\n",
    "            print(f\"  Run {run + 1}/{num_runs}...\")\n",
    "            run_results = train_model(\n",
    "                vqc,\n",
    "                torch.tensor(x_train, dtype=torch.float).unsqueeze(-1),\n",
    "                torch.tensor(y_train, dtype=torch.float),\n",
    "                f\"VQC_{initial_state}-run{run + 1}\",\n",
    "            )\n",
    "            pending_models.append(vqc)\n",
    "            model_runs.append(run_results)\n",
    "\n",
    "        # Find and keep the best model for each initial state (lowest final MSE)\n",
    "        index = torch.argmin(\n",
    "            torch.tensor([model_run[\"train_mses\"][-1] for model_run in model_runs])\n",
    "        )\n",
    "\n",
    "        models.append(pending_models[index])\n",
    "        # Store all runs for this model\n",
    "        results[f\"VQC_{initial_state}\"] = {\n",
    "            \"runs\": model_runs,\n",
    "            \"color\": color,\n",
    "        }\n",
    "\n",
    "    return results, models\n",
    "\n",
    "\n",
    "# Define training parameters\n",
    "num_runs = 3\n",
    "initial_states = [[1, 0, 0], [1, 1, 0], [1, 1, 1]]\n",
    "colors = [\"blue\", \"orange\", \"red\"]\n",
    "\n",
    "# Train all models\n",
    "all_results, models = train_models_multiple_runs(\n",
    "    initial_states, colors, x, g, num_runs=num_runs\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e685a334447f4a1e",
   "metadata": {},
   "source": [
    "## 4. Plot training loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "f7162c5436e42a80",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-10T09:03:48.574976500Z",
     "start_time": "2025-11-10T09:03:48.288014700Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 1000x600 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 0 Axes>"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_training_curves(all_results):\n",
    "    \"\"\"\n",
    "    Plot training curves for all model variants with average and envelope.\n",
    "\n",
    "    Args:\n",
    "        all_results (dict): Dictionary containing training results for all models\n",
    "    \"\"\"\n",
    "    fig, ax = plt.subplots(1, 1, figsize=(10, 6))\n",
    "\n",
    "    # Plot each model's results\n",
    "    for model_name, model_data in all_results.items():\n",
    "        color = model_data[\"color\"]\n",
    "        linestyle = \"-\"\n",
    "\n",
    "        # Get data from all runs\n",
    "        losses_runs = [run[\"losses\"] for run in model_data[\"runs\"]]\n",
    "\n",
    "        # Calculate mean values across all runs\n",
    "        epochs = len(losses_runs[0])\n",
    "        mean_losses = [\n",
    "            sum(run[i] for run in losses_runs) / len(losses_runs) for i in range(epochs)\n",
    "        ]\n",
    "\n",
    "        # Calculate min and max values for the envelope\n",
    "        min_losses = [min(run[i] for run in losses_runs) for i in range(epochs)]\n",
    "        max_losses = [max(run[i] for run in losses_runs) for i in range(epochs)]\n",
    "\n",
    "        # Plot mean line\n",
    "        ax.plot(\n",
    "            mean_losses, label=model_name, color=color, linestyle=linestyle, linewidth=2\n",
    "        )\n",
    "\n",
    "        # Plot envelope showing variance across runs\n",
    "        ax.fill_between(range(epochs), min_losses, max_losses, color=color, alpha=0.2)\n",
    "\n",
    "    # Customize plot\n",
    "    ax.set_title(\"Training Loss (MSE)\", fontsize=14, pad=10)\n",
    "    ax.set_xlabel(\"Epoch\", fontsize=12)\n",
    "    ax.set_ylabel(\"Loss (MSE)\", fontsize=12)\n",
    "    ax.legend(fontsize=10, bbox_to_anchor=(1.05, 1), loc=\"upper left\")\n",
    "    ax.grid(True, linestyle=\"--\", alpha=0.7)\n",
    "    ax.spines[\"top\"].set_visible(False)\n",
    "    ax.spines[\"right\"].set_visible(False)\n",
    "\n",
    "    plt.tight_layout()\n",
    "    # plt.savefig(\"./results/expressive_power_vqc_loss.png\")  # Uncomment to save locally\n",
    "    plt.show()\n",
    "    plt.clf()\n",
    "\n",
    "\n",
    "# Plot training curves\n",
    "plot_training_curves(all_results)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f6478657dd87945",
   "metadata": {},
   "source": [
    "## 5. Summary of results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "196c3c06801ddf01",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-10T09:03:48.601975100Z",
     "start_time": "2025-11-10T09:03:48.587448900Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "----- Model Comparison Results -----\n",
      "\n",
      "VQC_[1, 0, 0]:\n",
      "  Final train MSE: 3.911576 ± 0.002650 (min: 3.908155, max: 3.914612)\n",
      "\n",
      "VQC_[1, 1, 0]:\n",
      "  Final train MSE: 2.273466 ± 0.005170 (min: 2.268863, max: 2.280687)\n",
      "\n",
      "VQC_[1, 1, 1]:\n",
      "  Final train MSE: 0.012468 ± 0.017633 (min: 0.000000, max: 0.037405)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "def print_summary_statistics(all_results):\n",
    "    \"\"\"\n",
    "    Print summary statistics for all models.\n",
    "\n",
    "    Args:\n",
    "        all_results (dict): Dictionary containing training results for all models\n",
    "    \"\"\"\n",
    "    print(\"\\n----- Model Comparison Results -----\\n\")\n",
    "\n",
    "    for model_name, model_data in all_results.items():\n",
    "        # Calculate statistics across runs\n",
    "        final_mses = [run[\"train_mses\"][-1] for run in model_data[\"runs\"]]\n",
    "        avg_mse = sum(final_mses) / len(final_mses)\n",
    "        min_mse = min(final_mses)\n",
    "        max_mse = max(final_mses)\n",
    "        std_mse = (\n",
    "            sum((mse - avg_mse) ** 2 for mse in final_mses) / len(final_mses)\n",
    "        ) ** 0.5\n",
    "\n",
    "        print(f\"{model_name}:\")\n",
    "        print(\n",
    "            f\"  Final train MSE: {avg_mse:.6f} ± {std_mse:.6f} (min: {min_mse:.6f}, max: {max_mse:.6f})\"\n",
    "        )\n",
    "        print()\n",
    "\n",
    "\n",
    "# Print summary statistics\n",
    "print_summary_statistics(all_results)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90d96ce0b3d2403b",
   "metadata": {},
   "source": [
    "## 6. Visualize learned functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "dd277788a5a12877",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-10T09:03:48.908656500Z",
     "start_time": "2025-11-10T09:03:48.607731500Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 800x400 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 0 Axes>"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def visualize_learned_function(models, names, colors, x, g):\n",
    "    \"\"\"\n",
    "    Visualize learned functions of different models compared to the target function g(x).\n",
    "\n",
    "    Args:\n",
    "        models (list): List of trained models\n",
    "        names (list): List of model names\n",
    "        colors (list): List of colors for each model\n",
    "        x (np.array): Input domain\n",
    "        g (np.array): Target function values\n",
    "    \"\"\"\n",
    "    plt.figure(figsize=(8, 4))\n",
    "    plt.scatter(x, g, label=\"g(x) (target)\", s=30)\n",
    "\n",
    "    for model, name, color in zip(models, names, colors, strict=False):\n",
    "        model.eval()\n",
    "        with torch.no_grad():\n",
    "            output = model(torch.tensor(x, dtype=torch.float).unsqueeze(-1))\n",
    "        plt.plot(x, output.detach().numpy(), label=name, color=color, linewidth=3)\n",
    "\n",
    "    plt.title(\"Comparison: Target Fourier Series vs VQCs with Different Photon Numbers\")\n",
    "    plt.xlabel(\"x\")\n",
    "    plt.ylabel(\"g(x)\")\n",
    "    plt.grid(True, alpha=0.3)\n",
    "    plt.legend()\n",
    "    plt.tight_layout()\n",
    "    # plt.savefig(\"./results/expressive_power_of_the_VQC.png\")  # Uncomment to save locally\n",
    "    plt.show()\n",
    "    plt.clf()\n",
    "\n",
    "\n",
    "# Define model parameters\n",
    "names = [\"VQC_[1, 0, 0]\", \"VQC_[1, 1, 0]\", \"VQC_[1, 1, 1]\"]\n",
    "colors = [\"blue\", \"orange\", \"red\"]\n",
    "\n",
    "# Visualize results\n",
    "visualize_learned_function(models, names, colors, x, g)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "458e4340f599f728",
   "metadata": {},
   "source": [
    "Hence, this result demonstrates that a quantum model with more input photons is more expressive. [This paper](https://arxiv.org/abs/2107.05224) explains this phenomena by the fact that quantum models with more input photons have access to more basis functions, so they can learn Fourier series with  higher frequencies."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
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