{
 "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": null,
   "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 ComputationSpace, MeasurementStrategy, QuantumLayer"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6f7fa599036c74f",
   "metadata": {},
   "source": [
    "## 1. Define input domain, x, and target function g(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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": 3,
   "id": "3f27964b6712204d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-10T08:59:02.329037500Z",
     "start_time": "2025-11-10T08:59:00.330803400Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "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": 4,
   "id": "f65611c13781e51c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-10T08:59:02.397888200Z",
     "start_time": "2025-11-10T08:59:01.487951800Z"
    }
   },
   "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=\"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",
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       "<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",
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       "<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>"
      ],
      "text/plain": [
       "<drawsvg.drawing.Drawing at 0x137d7f800>"
      ]
     },
     "execution_count": 4,
     "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: (\n",
    "            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",
    "        ),\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: (\n",
    "            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",
    "        ),\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": 5,
   "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": 6,
   "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",
    "        measurement_strategy=MeasurementStrategy.probs(\n",
    "            computation_space=ComputationSpace.FOCK\n",
    "        ),\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": 7,
   "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": 8,
   "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: 4.2716, Train MSE: 3.9098: 100%|██████████| 120/120 [00:02<00:00, 59.22it/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: 4.2959, Train MSE: 3.9107: 100%|██████████| 120/120 [00:01<00:00, 60.77it/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: 4.2725, Train MSE: 3.9100: 100%|██████████| 120/120 [00:01<00:00, 63.14it/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: 2.5035, Train MSE: 2.2754: 100%|██████████| 120/120 [00:02<00:00, 58.75it/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: 2.5070, Train MSE: 2.2711: 100%|██████████| 120/120 [00:02<00:00, 59.01it/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: 2.5129, Train MSE: 2.2717: 100%|██████████| 120/120 [00:02<00:00, 58.95it/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: 0.0000, Train MSE: 0.0000: 100%|██████████| 120/120 [00:02<00:00, 54.67it/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 [00:02<00:00, 56.07it/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 [00:02<00:00, 57.27it/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": 9,
   "id": "f7162c5436e42a80",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-10T09:03:48.574976500Z",
     "start_time": "2025-11-10T09:03:48.288014700Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "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": 10,
   "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: 3.910163 ± 0.000415 (min: 3.909757, max: 3.910732)\n",
      "\n",
      "VQC_[1, 1, 0]:\n",
      "  Final train MSE: 2.272722 ± 0.001896 (min: 2.271118, max: 2.275384)\n",
      "\n",
      "VQC_[1, 1, 1]:\n",
      "  Final train MSE: 0.000007 ± 0.000010 (min: 0.000000, max: 0.000021)\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": 11,
   "id": "dd277788a5a12877",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-10T09:03:48.908656500Z",
     "start_time": "2025-11-10T09:03:48.607731500Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 0 Axes>"
      ]
     },
     "metadata": {},
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   ],
   "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."
   ]
  }
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