{
 "cells": [
  {
   "cell_type": "raw",
   "id": "3f258190",
   "metadata": {
    "vscode": {
     "languageId": "raw"
    }
   },
   "source": [
    "---\n",
    "title: \"Variational Quantum Circuits\"\n",
    "description: \"An introduction to parameterized quantum circuits, the parameter-shift rule, and barren plateaus — with working code examples.\"\n",
    "date: \"2024-03-01\"\n",
    "author: \"Your Name\"\n",
    "categories: [quantum-ml, vqa, pennylane]\n",
    "jupyter: python3\n",
    "execute:\n",
    "  enabled: true\n",
    "  freeze: false\n",
    "format:\n",
    "  html:\n",
    "    other-links:\n",
    "      - text: \"Download notebook\"\n",
    "        icon: download\n",
    "        href: variational-circuits.ipynb\n",
    "    resources:\n",
    "      - variational-circuits.ipynb\n",
    "    code-fold: true\n",
    "    code-summary: \"Show code\"\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ab37d6b",
   "metadata": {},
   "source": [
    "## Overview\n",
    "\n",
    "A *variational quantum circuit* (VQC) is a parameterized quantum circuit\n",
    "$$U(\\boldsymbol{\\theta}) = \\prod_{l=1}^{L} U_l(\\theta_l)$$\n",
    "where each $U_l$ is a unitary gate that depends on a classical parameter $\\theta_l \\in \\mathbb{R}$.\n",
    "\n",
    "The goal is to minimize a cost function\n",
    "$$\\mathcal{L}(\\boldsymbol{\\theta}) = \\langle 0 | U^\\dagger(\\boldsymbol{\\theta})\\, H\\, U(\\boldsymbol{\\theta}) | 0 \\rangle$$\n",
    "where $H$ is a Hermitian observable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a602a09c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Libraries loaded.\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Apply a dark style that matches the site\n",
    "plt.rcParams.update({\n",
    "    'figure.facecolor': '#111118',\n",
    "    'axes.facecolor': '#1a1a24',\n",
    "    'axes.edgecolor': '#1a1a24',\n",
    "    'axes.labelcolor': '#8888aa',\n",
    "    'xtick.color': '#8888aa',\n",
    "    'ytick.color': '#8888aa',\n",
    "    'grid.color': '#1a1a24',\n",
    "    'text.color': '#e8e8f0',\n",
    "    'font.family': 'monospace',\n",
    "})\n",
    "\n",
    "print('Libraries loaded.')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "faaac28c",
   "metadata": {},
   "source": [
    "## The Parameter-Shift Rule\n",
    "\n",
    "For gates of the form $U(\\theta) = e^{-i\\theta G/2}$ where $G^2 = I$,\n",
    "the gradient can be computed exactly via two circuit evaluations:\n",
    "\n",
    "$$\\frac{\\partial \\mathcal{L}}{\\partial \\theta_k} = \\frac{1}{2}\\left[\\mathcal{L}\\!\\left(\\theta_k + \\frac{\\pi}{2}\\right) - \\mathcal{L}\\!\\left(\\theta_k - \\frac{\\pi}{2}\\right)\\right]$$\n",
    "\n",
    "Below we simulate this for a simple 1-qubit expectation value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "91b80ca7",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1056x384 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Simulate <Z> = cos(theta) for a single RY gate applied to |0>\n",
    "def expectation(theta):\n",
    "    \"\"\"<Z> after RY(theta)|0>\"\"\"\n",
    "    return np.cos(theta)\n",
    "\n",
    "def parameter_shift_grad(theta):\n",
    "    \"\"\"Exact gradient via parameter-shift rule.\"\"\"\n",
    "    return 0.5 * (expectation(theta + np.pi/2) - expectation(theta - np.pi/2))\n",
    "\n",
    "thetas = np.linspace(-np.pi, np.pi, 300)\n",
    "cost   = expectation(thetas)\n",
    "grad   = parameter_shift_grad(thetas)\n",
    "true_g = -np.sin(thetas)  # analytical derivative\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(11, 4))\n",
    "\n",
    "# Left: cost landscape\n",
    "ax1.plot(thetas, cost, color='#6ee7b7', linewidth=2, label=r'$\\langle Z \\rangle$')\n",
    "ax1.axhline(0, color='#8888aa', linewidth=0.5, linestyle='--')\n",
    "ax1.set_xlabel(r'$\\theta$')\n",
    "ax1.set_ylabel(r'$\\langle Z \\rangle$')\n",
    "ax1.set_title('Cost landscape', color='#e8e8f0')\n",
    "ax1.legend(framealpha=0)\n",
    "ax1.set_facecolor('#1a1a24')\n",
    "\n",
    "# Right: gradient\n",
    "ax2.plot(thetas, grad,   color='#fbbf24', linewidth=2,   label='Parameter-shift')\n",
    "ax2.plot(thetas, true_g, color='#6ee7b7', linewidth=1.5, linestyle='--', label='Analytical')\n",
    "ax2.axhline(0, color='#8888aa', linewidth=0.5, linestyle='--')\n",
    "ax2.set_xlabel(r'$\\theta$')\n",
    "ax2.set_ylabel(r\"$\\partial\\mathcal{L}/\\partial\\theta$\")\n",
    "ax2.set_title('Gradient', color='#e8e8f0')\n",
    "ax2.legend(framealpha=0)\n",
    "ax2.set_facecolor('#1a1a24')\n",
    "\n",
    "fig.suptitle('Single-qubit VQC: RY gate', color='#e8e8f0', fontsize=12, y=1.01)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f17fed9",
   "metadata": {},
   "source": [
    "## Barren Plateaus\n",
    "\n",
    "A central challenge in training VQCs is the **barren plateau** phenomenon:\n",
    "for deep random circuits on $n$ qubits, the variance of the gradient vanishes exponentially,\n",
    "$$\\text{Var}\\!\\left[\\frac{\\partial \\mathcal{L}}{\\partial \\theta_k}\\right] \\in O(2^{-n}).$$\n",
    "\n",
    "The plot below illustrates how gradient variance decays with circuit depth."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bc3416c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 768x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "\n",
    "n_qubits_list = np.arange(1, 14)\n",
    "# Gradient variance decays as ~2^(-n) for global cost functions\n",
    "variance = 2.0 ** (-n_qubits_list.astype(float)) * 0.5\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 4.5))\n",
    "\n",
    "ax.semilogy(n_qubits_list, variance,\n",
    "            color='#fbbf24', linewidth=2.5, marker='o',\n",
    "            markersize=6, markerfacecolor='#0a0a0f',\n",
    "            markeredgecolor='#fbbf24', markeredgewidth=1.5)\n",
    "\n",
    "ax.fill_between(n_qubits_list, variance, alpha=0.15, color='#fbbf24')\n",
    "\n",
    "ax.set_xlabel('Number of qubits $n$')\n",
    "ax.set_ylabel(r'$\\text{Var}[\\partial\\mathcal{L}/\\partial\\theta]$ (log scale)')\n",
    "ax.set_title('Barren Plateau: gradient variance vs. system size', color='#e8e8f0')\n",
    "ax.set_xticks(n_qubits_list)\n",
    "ax.grid(True, alpha=0.2, color='#8888aa')\n",
    "ax.set_facecolor('#1a1a24')\n",
    "\n",
    "# Annotation\n",
    "ax.annotate('Exponential decay $\\\\propto 2^{-n}$',\n",
    "            xy=(7, variance[6]), xytext=(9, variance[2]),\n",
    "            arrowprops=dict(arrowstyle='->', color='#6ee7b7', lw=1.2),\n",
    "            color='#6ee7b7', fontsize=9)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d8f3f40",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "| Concept | Key result |\n",
    "|---|---|\n",
    "| Parameter-shift gradient | Exact, hardware-compatible |\n",
    "| Barren plateaus | Variance $\\propto 2^{-n}$ for global cost |\n",
    "| Mitigation strategies | Local cost functions, structured ansätze, QNGO |\n",
    "\n",
    "Next: **Noise-resilient gradient estimation** — how shot noise and hardware errors compound with barren plateaus."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
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