{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0adae4e7",
   "metadata": {
    "id": "0adae4e7"
   },
   "source": "# QCCM-601: Practical Quantum Chemical Simulation on Advanced Global Hardware\n\n**Special Graduate Enrichment Module**  \n**4-Week Live-Streamed Guest Lecture Series**\n\n**Instructor:** Joseph Volkan Ozcan, PhD Candidate & Quantum Computing Ambassador  \n**Contact:** [LinkedIn](https://www.linkedin.com/in/sapyoda/) | Quantum Task Force\n\n---\n\n### Course Overview\nThis notebook is a complete, end-to-end, fully executable educational implementation of the QCCM-601 syllabus.  \nIt is enriched with **diagrams, circuit drawings, molecular illustrations, heatmaps, workflow charts and comparative plots** so that every major concept is visualized.\n\n**Topics covered**\n- Molecular Hamiltonians & active-space methods\n- VQE + qEOM for ground and excited states\n- Quantum Machine Learning for materials\n- Quantum dynamics, error mitigation, and IP strategy\n- Clear pathways to IBM Condor (1,121 qubits), Origin Wukong, and D-Wave hardware\n\n**How to use in Google Colab**\n1. Runtime → Change runtime type → Prefer GPU (optional).\n2. Run the **Installation** cell first.\n3. Execute cells sequentially. Plots appear inline.\n4. Real hardware access requires separate cloud accounts; simulators are used by default.\n"
  },
  {
   "cell_type": "markdown",
   "id": "f0258348",
   "metadata": {
    "id": "f0258348"
   },
   "source": "## 0. Environment Installation & Verification\n\nRun this cell once. It installs the full stack and configures a consistent plotting style used throughout the notebook.\n"
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6889bb6c",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "6889bb6c",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1786421990610,
     "user_tz": -180,
     "elapsed": 48947,
     "user": {
      "displayName": "Joseph Volkan ÖZCAN",
      "userId": "11389530967736397480"
     }
    },
    "outputId": "0d3b9014-002b-4c29-a6da-c8737a3970fb"
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Python: 3.12.13\n",
      "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m1.8/1.8 MB\u001b[0m \u001b[31m18.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
      "\u001b[?25h\n",
      "Installation complete. Verifying imports and setting plot style...\n",
      "Qiskit              : 2.3.0\n",
      "Qiskit Nature       : 0.8.0\n",
      "PySCF               : 2.14.0\n",
      "PennyLane           : 0.45.1\n",
      "All packages ready. Plotting style configured.\n"
     ]
    }
   ],
   "source": "# =============================================================================\n# QCCM-601 - Full Software Stack + Plotting Style\n# =============================================================================\nimport sys\nprint(f\"Python: {sys.version.split()[0]}\")\n\n%pip install -q --upgrade pip\n%pip install -q \"qiskit>=1.0\" qiskit-aer qiskit-algorithms \\\n               \"qiskit-nature[pyscf]>=0.7\" qiskit-machine-learning \\\n               pyscf pennylane pennylane-qiskit \\\n               matplotlib seaborn pandas scikit-learn tqdm ipywidgets networkx pylatexenc\n\nprint(\"\\nInstallation complete. Verifying imports and setting plot style...\")\n\nimport qiskit, qiskit_nature, qiskit_algorithms, pyscf, pennylane as qml\nimport numpy as np\nimport pandas as pd\nimport matplotlib.pyplot as plt\nimport matplotlib.patches as mpatches\nfrom matplotlib.patches import FancyBboxPatch, FancyArrowPatch, Circle, Rectangle, Ellipse\nimport seaborn as sns\n\n# Consistent teaching style\nplt.rcParams.update({\n    \"figure.figsize\": (9, 5),\n    \"axes.grid\": True,\n    \"grid.alpha\": 0.3,\n    \"font.size\": 11,\n    \"axes.titlesize\": 13,\n    \"axes.labelsize\": 11,\n    \"figure.facecolor\": \"white\",\n    \"axes.facecolor\": \"#fafafa\",\n})\nsns.set_palette(\"colorblind\")\n\nprint(f\"Qiskit              : {qiskit.__version__}\")\nprint(f\"Qiskit Nature       : {qiskit_nature.__version__}\")\nprint(f\"PySCF               : {pyscf.__version__}\")\nprint(f\"PennyLane           : {qml.__version__}\")\nprint(\"All packages ready. Plotting style configured.\")\n\n# Safe circuit drawer (falls back to text if pylatexenc/mpl unavailable)\ndef safe_circuit_draw(circuit, title=None, fold=40, **kwargs):\n    try:\n        fig = circuit.draw(output=\"mpl\", style=\"iqp\", fold=fold, **kwargs)\n        if title:\n            import matplotlib.pyplot as plt\n            plt.suptitle(title, fontsize=12, fontweight=\"bold\", y=1.01)\n            plt.tight_layout()\n            plt.show()\n        return fig\n    except Exception as e:\n        print(f\"[Circuit draw fallback - {type(e).__name__}] Using text drawer instead.\")\n        print(circuit.draw(output=\"text\", fold=fold))\n        return None\n"
  },
  {
   "cell_type": "markdown",
   "id": "cc493cd6",
   "metadata": {
    "id": "cc493cd6"
   },
   "source": "---\n# Week 1: Molecular Hamiltonians & Active Space Mapping\n\n### Theoretical Content\n- Second Quantization and Fermionic Operators\n- Molecular Hamiltonian formulation\n- Jordan-Wigner, Parity, and Bravyi-Kitaev mappings\n- Classical pre-processing limits and active-space reduction\n- Mapping reduced problems onto physical qubit topologies (IBM Condor heavy-hex, Origin Wukong)\n\n### Hands-on Goals\n1. Build electronic structure problems with PySCFDriver\n2. Apply `ActiveSpaceTransformer`\n3. Compare qubit counts and Pauli-term counts across mappers\n4. Visualize molecules, active spaces, and hardware topologies\n"
  },
  {
   "cell_type": "markdown",
   "id": "03d4bd2d",
   "metadata": {
    "id": "03d4bd2d"
   },
   "source": "### 1.1 Building the Electronic Structure Problem & Molecular Visualization\n"
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "677c9d08",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 461
    },
    "id": "677c9d08",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1786421992911,
     "user_tz": -180,
     "elapsed": 1909,
     "user": {
      "displayName": "Joseph Volkan ÖZCAN",
      "userId": "11389530967736397480"
     }
    },
    "outputId": "8433b87f-afe1-47ae-de52-bb6ac0cb6606"
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "============================================================\n",
      "FULL LiH PROBLEM (STO-3G)\n",
      "============================================================\n",
      "Particles (alpha, beta) : (2, 2)\n",
      "Spatial orbitals        : 6\n",
      "Qubits (Jordan-Wigner)  : 12\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 1200x380 with 3 Axes>"
      ],
      "image/png": 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r6+GHH1avXr3suAeAOSyGYRj2DgIAgPvRhQsXtGPHDkVGRio5OVmZmZlyc3NTsWLFVL9+fVWtWlWOjo72DhMAAAAwDT2iAADIJwkJCVqwYIGWL1umHdtDdfrsOUmSo4OD3Fyc5OhgUWp6plLTMyRJRYu4q17demrVpo2GDh2qKlWq2DN8AABwBwzD0IkTJ7Rjxw5t375d23fs0Okzp5WSkiJJcnNzU1DpIDVq2FCNGjVSw4YNFRwcLIvFYufIAfugRxQAAHfp0KFDmjFjhubOma0rCYlqWr646pT2Ue3SPqpVyldlfIvY/LMZn5ym/WdjrT9/H49SbGKKOnZ8SK+8MlzdunWTkxPfFQEAUJjFxsZq/vz5mjp9mo4cDpckefh5yru8n4oU95Sjy9W/5ZlpGUq6dEVxEdFKiL4iSapctYqGD3tFAwcOlI+Pj712AbALElEAANyh+Ph4jR49WrNmzZKfp7t61y+jPo3LK8i36G3Vk5qeqWX7T+u70EjtPhmlGtWqau78b9S4ceMCihwAANypc+fOady4cZr/zTdKS0tV6cblVbZVZRWrVEJuPkVuuG1KbJIuH72okxuP6ExohFxdXDVgwACNGzdOgYGBJu0BYF8kogqp7N07d+7cqYsXLyo1NVUuLi7y8/NT/fr11bBhQ1WqVEkODg72Dhe4oUuXLmnHjh3WuXJSUlLk6OgoT09P1apVSw0bNlTt2rXl4uJi71CBW7Z69Wo9N3SILkdH6Y1O1fVUw2C5Ot39fE97Tl/We7/vVdjZWL3xxhsaN26cXF1d8yFiAABwNwzD0LfffqvhI4YrXZmq8HANle9QTe63+QXUNcmXExWx9qCOrz4oF4uTpn4xVf369WPIHu57JKIKmePHj+vLL7/U7DlzFR11SZJU1Ntfbh5+cnBwkpGVqdSkGF2JuSBJ8vLy1oAB/fXyyy+rZs2a9gwdsBETE6N58+Zpxpf/p/DDhyRJru4e8vANlMXRRTKylJGaqPjoM8rKypSzs4u6dn1Ur7zyijp06ECCFYVWZmamRo8erc8//1wtKgXok+71brsH1M2kZ2bpqw3h+mLtYVWpUlm/L1+h4ODgfG0DwFUZGRk6d+6ckpKS5OjoKB8fH/n7+9s7LNxjDMPQxYsXFR8fL8MwVLRoUQUGBvL/zH3k/Pnzeu7557Ts92Uq27Ky6g1uKVdPt3ypO/VKinbP/Vsn/z6ixx57TDNnzlRAQEC+1A37y8rK0rlz55SYmCiLxSIvLy+VKFHigU44kogqJA4dOqRXR4/WqpUr5eLuoVLV2sm/bF35BFSSa1GfHOXTkuMVd/G4ok/t09mwECUlxKh16zaaPPm/atiwofk7APxPbGysxo4dq7lz5yk9PV0lKzdXQMWm8g6oqCLeJXPccDPTUxV/6YRizh3S2YNrFXvxhCpWqqyPxn+op59++oG+QaPwSU9P16CBA7Vo8SK926WOBjarUKDn6OHzcXr5+1BlOBfRH2tCVL169QJrC3hQGIahv/76Sz///LO2bgvVnj17lJKcZFMmoGSgmjRupBYtWmjAgAEqXbq0naJFYXb8+HF988032rJli7aFbtfl6Cib9UWLeqhBgwZq0qSx+vTpo0aNGtkpUtytY8eOqUPHhxQVF616Q1uqdOPyBdLOmdAI7Z79t/y9/bR2TYgqVKhQIO2g4IWGhmrRokXati1UO3fuVGJigs16P//iatyooZo1a6YBAwY8cO81iSg7y8zM1OTJk/XOO+/K1cNPFRr1UqmqreTofOvDMLIy03X+6FYd3/6zrkRF6q233tI///lPhnLAdMuXL9fQZ59TTGy8yjforjK1O8mtqO8tb28Yhi6fCVPEzqU6f3SrevTooRkzZvCNEAqFrKwsDejfXz/8sFhTnmqkzjXN+WB68UqyBs/frPgsF23ctPmB+0cFyC9paWn6+uuv9cXUaTp0MEyeviXlWaKyvAMqytOvjByd3WRkZSktOU5xFyN05dIxxZw7rKyMNHXv3l2vvfaaWrRoYe/dQCGwevVq/XfyZK1etUoubkXlE1hNXsUryKtEeTm7ecgiizLSk3Ul6qTiLh5T/PnDSoyPVoOGjTRq5Aj169dPjo53P5Qb5jh27JhatmqpFId0tXq7i4r4exZoe0lRV7Tx4+Vyy3LR3xv/VsWKFQu0PeSfzMxMfffdd5ry2efatXOHinr5yatkVXmXqChP/7JycnaXIUPpKQmKvxih+EvHFXvukNJSEvXwI4/otdGj1alTJ3vvhilIRNlRdHS0Hn+8uzZv3qTyDR5T1Rb9bisBdb2szAwdDf1Jx7b+oKrVqmnliuUqU6ZMPkYM5C4zM1MjR47U9OnTFVC+gWp1fFnunsXvqs6z4Zt0cO1XcnW26Jdffla7du3yJ1jgDr355puaNGmiPuvdWI/WCjK17aiEFPWZtVGWor7auXuPvL29TW0fuNft2rVLAwYO0sGwMAVUbKJydbvIr0ztm/ZoTE9N0pmD63Rq7wrFRZ3Syy+/rAkTJsjDw8OkyFGYREdHa8SIkVq4cIGKBVZSmdpdbukLZCMrUxcjdujk3pW6ELFTzZu30Lx5c1W5cmWTIsedOnfunJo2b6b49AS1ea/bTScizy8psUn668Pf5eXsoa2btzCJ+T0gPDxcgwcP0ebNmxRQvoHK1u2iEsENZHG4cdI5Mz1VZw9v1Kl9K3T53FE980xfffHF5/Lz8zMpcvsgEWUnFy9eVNt27XXi5Bk16PamipWukW91x1+K0M7f/i1vDxdt+Gu9ypcvmK6jgHR1bo3+/ftr8eIfVKvDCypb55F8G6qUmhSnPSsmK/bcQS1Z8ou6dOmSL/UCt2vDhg1q27at3nykpp5vVcUuMZy6nKhu09eqd9/+mjVrll1iAO41hmHoP//5j9795z/l5VdWtToNl3eJ2+9VaBhZOrF7ucL//laBgSX1y88/qUGDBgUQMQqrtWvXqvfTfXQlIUnV2z6r0tXb3dH/O9GnD2j/n1OVlhijL774XM8//3wBRIv8YBiGOnfpor9D/1a7D7sXeE+o6yVFXdHaf/6qVk1aauWKFUxXUYjNnDlTI0aMlEtRX9XqOFx+Qbc/d7NhGDpzcJ0Orp8lT48iWrzoe7Vv374Aoi0cSETZQVxcnFq3aatjEafUpNeH8iiW/9+sJ1+JUujP78vX00WbN/1NFh0FwjAMDR06VPPnf6P6XV9XYOXm+d5GZka6di2fpJhTe7R69Sq1adMm39sAbiQpKUl1a9eSd1aCFg5tJUcH+/0j+H1ohN75dZdWrFihzp072y0O4F5gGIZee+01TZ48WZWaPKkqzZ+Wg6PzXdWZGHtOu1f8V+lXzmvVqpUM1XtA/P777+rZs5d8SlVX3UdGyc2j2F3Vl5GeorB1s3Vy32r9+9//1ptvvplPkSI/zZ49W88++6xavdFFgQ3K2SWGczsjtXHCCs2ePVtDhgyxSwy4sf/85z966623VLb2w6rRbqicnO9uAvuUhMvas+ozxZ07pJ9++lHdunXLp0gLFxJRdjBo0GB9v/hHNev9sbz8C+6mlhR/UVsWjVXL5g21auVKsujId3PmzNHQoUNVr/M/FFSjXYG1k5mRru1LxsuSelGHDobJ1/fW550C7tarr76qL6dN1e+vtFd5k78NvZ5hGBo8f5NOJDpof9hBhugBN/Dee+9p/PjxqtXhBQXXezTf6s1IS9b2X/+llNhIbdywQXXr1s23ulH4rFu3Tg8//Ij8gxuo/qOv3XUy8xrDMBS+aaGObF2sadOmadiwYflSL/LHqVOnVKNmDfk3KK3GL9u3V8q26SGK3nVWB8MOKijI3KkBcGPTpk3T8OHDVbnZ06rSvE++fd7OzEjX7hWfKjpyl1atWnlfTlHC80RNtmzZMs2fP0/V2wwt0CSUJBXxKqFaHYfpj9WrNXv27AJtCw+e06dPa+SoUSpTs32BJqEkydHJWXUeGaW4+ASNGvWPAm0LyO7s2bOaOvULjWhX1e5JKEmyWCz6pHt9Xbp0SV999ZW9wwEKrTVr1mj8+PGq1mpAviahJMnJxV2Nur8jpyLF9VTvp5WSkpKv9aPwiImJ0dN9npFPqWqq1yX/klDS1ft5lRbPKLh+N40cNUp79uzJt7px995+520ZzlLdAfbv9VhvYEsZztLYt8faOxRks3v3bo36xz9Uvn63fE1CSVc/+9Tr8pq8A6vq6T7PKCYmJt/qLixIRJkoPj5ezz73vAIqNFRQzQ6mtFmifEOVqfmQ/vHqqzp79qwpbeLB8MKLLyrL4qLqbZ81pT13Tz9VazNE33wzX8uXLzelTeDrr7+Ws6OD+jUtPE+qK+VTRF1qltKMaVOVlZVl73CAQufKlSsaPGSoipeto4qNexRIG04u7qrb+VUdP35c77//foG0AfsbOXKU4uISVOfhUXJ0yr8k1DUWi0U12gySZ7EgDRg4SOnp6fneBm7fpUuXtGjRIlXsUksuHvZ/CrmLh6sqdqmlRYsWKSoqyt7hQFefwjpg4NVrt3qbQQUy8sjRyVl1Hr56D7ofv4gnEWWiefPm6dKli6rV4SVTh8nVaDtEaelZmj59umlt4v62Z88erVi+XFVbDZaLm3lPDgqq0UH+QTX1r399bFqbeHClp6fr/2ZMV/fapeXplv8fQO5G/6YVFBF5UqtWrbJ3KECh88EHH+jCxUuq3ekVWSwF96+up18ZVW7WR5MmTdL+/fsLrB3YR0hIiL799htVaztU7p4F9/QqB0dn1eo0XAf279fnn39eYO3g1s2ePVuGYSi4XTV7h2IV3LaqDBmMcikkPv/8c4UdOKDanUbka0/J67l7+qla26tfxK9du7bA2rEHElEmMQxDX0ydppIVm8nd6+4ea3+7nN08VKpaO335f18pNTXV1LZxf5oxY4aKePkVyOTkN2KxWFS2Xldt2vS39u7da2rbePD8/vvvOnv+QqHqDXVNvSBf1SxdTNOnTbV3KEChkpiYqP/7v69Uts6jKuIdUODtVWjYXe4evpo6lWvxfjN5yhT5BJRXUI2Cnx/IJ6CSSldvqymffa7MzMwCbw95y8zM1LQZ0xXUvKJcPe9u0un85OrlrtLNKmjq9Gn0hrazzMxMTfnsc5Wu3lbeARULvL2gGh3kE1Bek6dMKfC2zEQiyiTr1q3TkfDDKlvXPk85Kle3s6KjLunnn3+2S/u4f8THx2v+N98oqGYnOTg6md5+yYpNVMTTTzNmzDC9bTxY/vjjD1UM8FGNQB97h5KDxWJRt1qlFBISwocWIJsFCxYoMTFR5eo+Ykp7Do5OKl2zk+Z/843i4uJMaRMFLzIyUsuXLVOZ2p1NG8VQrm4XnT51UitWrDClPeTuwIEDOhV5UuXaVrF3KDkEt6mqU5EndeDAAXuH8kBbvny5zpw+pXJ183f+wbxYLBaVqd1Zy37/XSdPnjSlTTOQiDLJ8uXLVdS7uPyCatmlfU+/MioWWIm5dXDX/vrrLyUnJal09XZ2ad/B0Uklq7TUb78ts0v7eHBsD92m2iXtP0F5XmqX9lVScooOHz5s71CAQmPO3HkqUb6BiniVMK3NsrUfVkpyin755RfT2kTBWrBggZycXVW6WhvT2vQpWVnFAitp7tx5prWJnHbs2CGLxaJiFc27h9wq34rFZbFYtGPHDnuH8kCbN2++igVWkk/JSqa1WbpaGzk5u+q7774zrc2CRiLKJKGh2+VVoqKpc0Ndz7NEJW3dtt1u7eP+sGPHDrkV9TJlyENefEpW0Zkzp3Tp0iW7xYD7W3p6uvbu3adapX3tHUqeapXykST+IQX+JyMjQ7t27pRfmTqmtuvmUUze/kHatm2bqe2i4GzZslXeJavIycXd1HZ9StfSli1bTW0Ttnbs2CGf0sXkVMjmhpQkZ3cXeZcqxt99O9u8eYt8S9c2tU0nF3d5l6ysrVvvn78z5o+reQAZhqGdO3eqVJ3H7BqHd0Al7ftjlSIiIuThYd4E07i/bNq0SV7F7ZtU9S5xdTz2jh071LmzfYa74v4WFham1LQ01f5fsqcw8nRzVrniXtq4cSPXAaCr121KSrIpc3Zcr6h/BW0L5cu++0Vo6HZ5lW5iers+AZW0c/sSHTp0SH5+BTdBOvK2afMmeQYXs3cYefIqX0ybNm/iy1g7iYqK0tmzp9Wgfh/T2/YsXkGh99HfGRJRJjh37pyuXImXl385u8bh5V9OhmGoQoXCN/Eu7h0WB0eVr9/NrjEU8SkpJ2dXHTx4kA/gKBBnz56VJJX2LWLnSG4syMtVX331lb766it7hwIUGl7Fg01v07tEee3fstD0dpH/4uLidO7cGdWvX970tr2KX22zevXqpreNqyyOFlV/ooG9w8iTR4CXdi3ZpRIlCt/QwQfJtWvVTN7Fy+v49iWKi4uTt7e36e3nN4bmmSApKUmS5Ghy997rmd29GPcve59LFotFzq7u1msLyG/JycmSJDdnRztHcmPuznyfBFzPycX8BLKzq4dSU1OUkZFhetvIX1euXJF09T01m7NrUdPbxHUMydGl8P5tdXRxkgzD3mE88JzdzL9Wnd2u3pMSEhJMb7sgkIgygVFobhb2G0qF+439zyWLLIXo2sL95tq5ZSkE5/qN2HGELFBI2emi+F+z/F2699n1PeSeDiBPV28QWVlZdo4jf5CIMoG7+9XeI5npqXaNIzM9xa7t4/5h73PJMAylp6VYry0gv107t1IzMu0cyY0lpxXu+ADzGcrMMP//rYy0ZDk5O8vZufBNcIzbU7To1Z4OGenJpredkWZ+m7iOxaLM9ML7tzUzLYNvoQoBe1yr1+5J1+5R97rC2+/wPhIYGCg39yJKuHxaARUa2S2OK5dPS5LCw8Pl4+Njtzhwb3vqqd46fPq0XWNISYhSelqyKleubNc4cP8qXry4JOl8fLICvApvwvNiYroGDx6sCRMm2DsUwO52796thx9+WFcuRcq3VFVT246/FKlqVauZ2iYKhq+vr/z8i+vKpUipSktT246/FClJ2rNnjwIDA01tG1e1f6i9EqMK79CnpOgE1ahRQ2vXhNg7lAfS2bNnVa9ePV2JilRRH3Ov0SuXTsi/eAn5+hbeJzrfDhJRJnB0dFTdunV16sIxu8YRd+GoypUrz4d33JUWLZpr+zT7Towc979rqWHDhnaNA/ev2rVry8nJUfvPxKpuUOF8ek5SWoaOXojVmJYtrYkz4EHWpk0bOTk5K+7iMdMTUYlRx9Xp0bamtomCYbFY1LhRQ+0KP25623EXj8m/eAnVrl3brk8nfpA1b9pcv6xZau8w8hR/4rI6dXqCv/t24u/vLz//4oq7cEwlKzUzte34i8fVuFHD++bewNA8kzRt0lgJUfZNRF25eExNmza2awy49zVq1EiJ8dFKSbhstxhizx+Vf/ESKlWqlN1iwP3Nzc1NNWvU0P6zMfYOJU9h5+KUZRgkZIH/cXV1Va3atXX59AFT201LSVDspRNq1Mh+vd6Rvxo3bqy48+HKykw3td3Ys2Fq0rjRffNB817UsGFDxZyMujoErpDJTMtQ7Klo/u7bkcViUdMmjRVzNszUdjMz0hV3IVyNG98/n+VJRJnkoYceUnz0WcVeOGqX9pPiLyr6zCE99NBDdmkf94/WrVvLyclZZw9vtEv7hpGlC0c36eFOnfhHDQWqUeMm2n/+ir3DyNP+szFydXFRzZo17R0KUGj079dXF45vU2pSrGltnj4QIgeLg3r16mVamyhYffr0UUpSvM4d2WJam1eiTynq1AH169fPtDaRU6NGjZSVmaXYE1H2DiWH2BNRysrMIultZ3379lXUqQNKuGzeVCXnj25WStIV9enTx7Q2CxqJKJM8+uijKlU6SCf3rLRL+yf3rlbRokXVt29fu7SP+0fx4sX15JNP6vT+VTIM85/aEBW5R1cun9WwYS+b3jYeLG3btlXYmcuKjC6cc0WsPnheLZo3l4uLi71DAQqNwYMHy8nRUaf2rzGlPcPI0un9q/Tkk0+qRIkSprSJglejRg21adNWp/aZ93975N5V8vPzJ6FpZ3Xr1pV/cX+d3GSfzgM3cvLvo/Iv7q86derYO5QH2pNPPqlixfwUaeLn+lN7V6pt23aqXr26aW0WNBJRJnFyctKwl1/S2cMblJYcb2rbmRlpOhO2RkOGDJaHh4epbeP+9MorwxQffUaXTuw2ve3IPStUs1ZttWjRwvS28WB58skn5evjrQWhEfYOJYfwC/HaevyiXnyZhCyQnZ+fn/r166sTu5YqNSmuwNs7dSBE8dFnNGLE8AJvC+YaNWqkok4d0IXj2wu8rcTYczpz4E+99NKLcnV1LfD2kDdnZ2e98PwLOvXXUWWkmDs080YyUtJ1csMRvfjCizyd085cXV318ssv6fSBP5UYe67A27twfLuiTodp5MgRBd6WmUhEmej555+Xu5urwtbPMbXd8M3fKyM1USNG3F8nL+ynZcuWatykqQ79NVuZ6eY9JvvC8e06f2yb3nxjDMPyUODc3d019Nnn9OOuU0opZI9yXrDtuAKK+6tHjx72DgUodD7++GO5uzjqwNqCfbBG8pVLOvTXHA0aNJgvR+5DPXr00MOPPKIDITOUnlJwPWMNI0v7/piqwMCSeuuttwqsHdy6F154QekpaTq58Yi9Q7GK3HhEGSnpeuGFF+wdCiS99dZbKlkyQPv/nFagI0TSUhJ0IGSGHunc+b77n49ElIlKlCihzz6botNha3XheKgpbcacC9fx7Uv0wQfjeFoe8o3FYtHcObOVHH9RhzcvNKXN9Gw34v79+5vSJvDSSy8pNjFFv+w+ae9QrGKSUvXLntN6/sWXGJYH5CIgIEDTp0/T2cN/63TY2gJpIyszQ3tXT5Wvj5emTJlcIG3AviwWi2Z9/bUcjDTtX/N/BfZh89j2JYo6dUDz5s5h5EIhUa5cOXXt2lVHl+8rFJOWZ6Zl6NjyferWrZvKli1r73AgycPDQ/PmztGlk/t1fPuvBdKGYWRp/5ov5WCk6euZM++7L+FJRJls8ODB6tyliw6s+VLJVwp2Ery0lATtW/25GjRooDFjxhRoW3jw1KhRQ+PHf6iIHUt1KXJPgbZlGFnadx/fiFF4VapUSf379dPEPw7q4pVke4cjSfpw2V45ubrplVdesXcoQKH19NNPa/Dgwdr7x1SdP7YtX+vOyszQnlWfKeZMmBZ89618fHzytX4UHkFBQZr19dc6G75RB9bOkmEY+Vr/yX1/6NCG+Ro7dqzatWuXr3Xj7nzyySdKikrQgR/M6TxwI/sXhyopKkGffPKJvUNBNu3bt9fYsWN1cMM8ndz/Z77WbRiGDqydpXPhf2vW118rKCgoX+svDEhEmezatyu+3kW0/ZcPlJoYWyDtpKcmasev4+WYlaTvvvtWTk5OBdIOHmyvvfaaOnbqqJ2//VsxZw8VSBuGkaUDITN1LvxvzZ0z5768EaNwm/LZZ3Ir6ql/Lt2T7x9CbtfqsLNauueUPv9iqkqWLGnXWIDCzGKxaObMmXqie3ft/P0/ity7Ol+u37SUBO38fYLOH92sRYu+V4cOHfIhWhRmvXv31owZM3Ri9zLtXf25MtJT7rpOIytTR7f9qL1/TNNLL72kf/3rX/kQKfJTzZo19cG4DxS+bK+ij1ywWxzR4ed1ZPleffjBh6pRo4bd4kDu/vWvf+nFF1/U3tVTdXTbTzKy7n4qh4z0FO1Z9blO7F6mGTNmqHfv3vkQaeFjMez9X/UD6siRI2rVuo1SMhzV8PF3VdQ3MN/qTkm4rB1L/6XMpCiFhKxRw4YN861u4HqJiYnq3LmLtm7brvpdX1eJ8vl3vmVmpGn/mhk6HbZOM2fO1LPPPptvdQO3Y8mSJerRo4cm9WqkHvXt0y0+JilVXaauVbM27fXr0t/oGQjcgoyMDA0bNkwzZ85UQIVGqvXQy3L39Lujui4c26YDIf8nR6Vr0aLv1aVLl3yOFoXZt99+q+eff0HORXxUq+Nw+QXVvKN6EmLOat8fUxV9Okxvv/22PvroI+7nhVRGRoaaNW+mo2cj1O7D7nLxMHci+bSEVK1771dVLl1BmzdtpmNBIWUYht599119/PHH8g+qoVqdhsvDt9Qd1RV9ar/2/zlN6cmx+vrrmerXr18+R1t4kIiyo+PHj6tjp4d1+vQZVWnZX8H1HpXFcued1AzD0JmD63Rw/Sx5e3lo9aqVqlu3bj5GDOQuKSlJTz71lFYsX65ydTureutBcnJxv6s6Y86Fa/8fXygp7oLmzp2jvn375lO0wJ0ZOGCAfli8SHMHNlfjYH9T205MzdDg+ZsUeSVT+/YfUGBg/n15ATwIfvvtNz373POKi09QUM2HVK5Ol1v6EtDIytTFE7t0cs9yXYjYqc5duujrmTNVunRpE6JGYXPkyBENGjRYmzdvUmDl5ipX91H5lal1S4mk+EsnFLlnpc4cDFFQUJDmzZ2jNm3amBA17sbhw4fVrHkzOZdwV6uxj8rJzZwn1mWkpGvjJ8uVfjFZWzZvUdWqVU1pF3du/fr1GjR4iM6cOaPS1TuoXN3O8ioefNPtDMNQ9Kn9ityzXOeObFaLFi01d+6c+35+ZxJRdpaQkKA33nhDM2bMkH+ZmqrUtM8t/0G7xjAMxZ4/omPbftD5Y6F65pm++uKLz+Xnd2ff+AF3IisrSzNmzNCYN96Qo4unKjV7RoFVWsrR6fb+YCfFXVDEzt90Yvdy1a9fX/PmzVWtWrUKKGrg1qWkpOjRLp21fesWfd2/mRqVM+cem5iaoRcXbNW+81cUsnadGjdubEq7wP3m8uXL+uSTT/T117MUGxsj/zK15BNYVd4lKsrDr4ycnN1kGFlKS45X3MXjirtwVJdP71VCzAXVrVdfb74xRn369KH3ygMuMzNTs2bN0qf/nazww4fk5R8k39K15R1QUd7Fy8vZzUOyWJSZlqL4qEjFXTimuPMHFX3msEoElNSwl1/S66+/rqJFi9p7V3CLtm3bpvYdOqhoGW+1GPOIXIoWbM+otMRUbZqwUomn47Vu7Vr+7t9DEhMTNWnSJE2bPkOXLl6QX+mq8i5ZXd4BFeXlX06OLm6SYSg9JUFxlyIUd+GYYs7sU3zUaVWpWk2vjX5Vzz33nBwc7v8ZlEhEFRJr167Vy8Ne0eFDB+XtX1ZBtR6Wf7m68vAtJYuDY47yhpGlxNjzij61X6f3r1bM+aMqWy5Yn02ZrCeeeML8HQD+5/jx4xo27BWtWrVS7kV9VKrGQypZqam8igfL0Sn3J3ylJFxWzLlwnQlbowvHt8vDw1Nvvz1Wr7/+Ot2QUahcuXJF3bo+qm1bt+jz3o31ULWC7Zl08UqyXl4YqmOXk7Vs+Qq1bt26QNsDHgTJyclavHixfvzxR4WG7tCFC+dylHF0dFTVqtXVqlULPfvss2rcuDEJKNgwDEPr16/X3LlztWnzFh09Ep7rPGSlg8qqaZPGeuaZPurevbucnc3pUYP8tW3bNj3S+RGpqKMaDWsn3wrFC6Sdy8cuaseM9VJiplatXKUmTZoUSDsoWOnp6VqyZIm+/36Rtm4L1ZnTOZ++bLFYVKlyFbVo3kyDBw9W27ZtH6i/MySiCpFrf9CmTZumX5YsUWZGhpxd3OVdorxcihaTxcFJRlam0pNjFXfxuNJSEmWxWNSlSxe98soreuSRR+TomDNpBdjDoUOH9OWXX2r27Dm6ciVeDo6O8vYvJzevknJwcpFhZCkzNVEJ0SeUGB8tSapdp65GjhiuZ555hm8KUWglJyfrmT5P69elv6l3w2C93aW2PPO5q75hGFq655Q+WL5fbkU9tWzFCub7AwrIuXPndOTIESUnJ8vR0VE+Pj6qWbOm3N3vbog5HixXrlxRWFiY4uPjZRiGihQpomrVqsnf39yh3Cg4Bw8e1DN9n9G+fftU9fF6qt6zoRyd8+ezV2Z6psJ+2q7w3/aodu3aWrhgoapXr54vdcP+oqKidOjQISUlJcliscjLy0s1atSQp6envUOzGxJRhVRcXJx27typHTt2aMeOHbpw4aJSUlPl6uIif38/NWjQQA0bNlTDhg0ZgodCLTU1VXv37rWeyxEREUpKTpGzk5M8PT1Vp05t67lcrly5B+qbANy7DMPQzJkz9droV+XpbNFHj9dV28oB+XL+XohP1nu/79GfYWfV5+mn9cXUqXyQAQCgEEhPT9e///1vfTj+Q3mU9FaVx+oqqFkFObrcWQ/+zLQMndpyTEd+26uE83F675/v6a233qLnHO57JKIAALhDkZGRevbZoVqzJkQ1ShdTv0bl9HjdMipym/+QGoah7ZHR+nZbhFYdOCtfX1/N+L//U8+ePQsocgAAcKf27t2r0a+N1po/18jdq4jKtq2scq2ryCvIV5abzO9jZGUp/nSMIjeE6+T6I0qOT9JDHR/Sfz/9r+rUqWPSHuQtLCxMS5cuVUREhGJiYvT666/fdIjgoUOH9N133+nMmTNKTU1V8eLF1bFjR3Xr1s1aZvXq1Vq9erUuXbokSQoKCtKTTz6p+vXr3zSm6OhoDR8+XKVKldKnn356dzuIQoFEFAAAd8EwDK1evVrTpn6h35ctl4ebix6uFqC6QcVUu7SPqgZ4y/W6rvuGYehUTJL2n43R/jOxWnf0kg6fi1HlihU0bPgIDR48WD4+PvbZIQAAcEvCw8P15ZdfatbsWYqPi5ezm4t8g/3lFVxMRUt4WXtKZaZlKPFivOJPXFbMiSilp6TJy9tLzw59Vi+99JKqVKli5z35/3bt2qXDhw+rQoUKmjRp0i0loiIiInTmzBmVK1dOrq6uOnTokGbOnKlBgwapY8eOkqTt27fLwcFBgYGB1ilpli5dqgkTJqhMmTI3rP+nn37SmTNndPDgQY0ePfq+f6Lcg4BEFAAA+eTEiRP66quvtOz333Qg7KAyMzPl5Oig0sU85ebkKAcHi9IyMhWVkKK4xBRJUunAkmrZqrWef+EFdejQ4YF4UgoAAPeTpKQkbd26VTt27ND27du1LXSbzp+/oNSUq3/rXd3cVLJkgJo0bqJGjRqpYcOGatq0qYoUKWLnyG+sd+/et5SIys2kSZPk6uqqESNG5FlmyJAhGjBggDp06JBnGcMwNHLkSD377LM6cOCAEhIS9OKLL952PChceBwVAAD5JDg4WB9//LE+/vhjJScnW+dHi4yMVHJysjIzM+Xm5qZixYqpfv36atiwoQICAuwdNgAAuAtFihRR+/bt1b59e5vl1/p8PGhzoEZEROjw4cPq06dPruuzsrK0efNmpaam3rQ32IEDB5Samqo6deqoWLFi+uc//6lBgwbJzc2tIEKHSUhEAQBQANzd3dW0aVM1bdrU3qEAAAA7eNASUC+99JLi4+OVmZmpp556Sg899JDN+pMnT+qdd95Renq63Nzc9PrrrysoKOiGdYaEhKhFixZycHBQ2bJlVaJECW3ZskXt2rUrwD1BQSMRBQAAAAAA7sqHH36olJQUhYeHa8GCBSpZsqRatWplXV+qVClNnDhRSUlJ2rJli6ZNm6YPPvggz2RUYmKitm7dqvHjx1uXtW7dWiEhISSi7nEkogAAAAAAwF0pUaKEJKls2bKKi4vTDz/8YJOIcnJyUsmSJSVJFSpU0LFjx7R8+XK98MILuda3ceNGpaen6+2337YuMwxDhmHo7NmzKlWqVAHuDQoSiSgAAAAAAJBvDMNQRkbGDctkZWUpPT09z/UhISHq1q1bjt5Ps2bN0tq1a9WvX7/8CBV2QCIKAAAAAAAoJSVF58+ft76+ePGiTpw4IQ8PD/n7+0uSFixYoMuXL2v48OGSpJUrV8rf31+lS5eWJB08eFC//fabunTpYq1nwYIFqlevnvz9/ZWSkqKNGzcqLCxM77zzTq5xnDhxQhERERo5cqS13mtatmypH3/8UX369JGjo2O+7j/MQSIKAAAAAADo2LFj+uCDD6yv58+fL0lq27atXnnlFUlSTEyMoqKirGUMw9DChQt18eJFOTg4qGTJkurXr586duxoLRMXF6dp06YpJiZGRYoUUbly5fTOO++oTp06ucYREhKioKCgHEkoSWrSpIlmzZqlXbt2qVGjRvmy3zCXxbj2TEkAAAAAAACgADnYOwAAAAAAAAA8GEhEAQAAAAAAwBTMEQUAAO57YWFhWrp0qSIiIhQTE6PXX39dTZo0uel26enp+vHHH7VhwwbFxsbK19dXvXr1UocOHaxlNm/erEWLFunSpUvWeTEaNGhw07rT0tL04osvysHBQV9++aWcnZ3vah8BAADuBSSiAADAfS81NVXBwcHq0KGDJk2adMvbTZ48WXFxcXrppZdUsmRJxcbGKisry7r+8OHD+uyzz9S3b181aNBAGzdu1MSJE/Wf//xHZcuWvWHdW7ZsUZkyZWQYhkJDQ9WiRYs73j8AAIB7BYkoAABw36tfv77q169/W9vs3r1bYWFhmjp1qjw8PCRJJUqUsCmzfPly1atXT48//rgkqU+fPtq3b59WrlypF1544Yb1r127Vq1bt5ZhGAoJCSERBQAAHgjMEQUAAJCL7du3q2LFivr111/14osvatSoUZo/f77S0tKsZcLDw1W7dm2b7erWrasjR47csO7z588rPDxczZs3V4sWLXTw4EFdunSpQPYDAACgMCERBQAAkIsLFy7o0KFDOnXqlMaMGaNBgwZp69at+vrrr61lYmNj5e3tbbOdt7e3YmNjb1j32rVrVa9ePXl4eMjDw0N169bV2rVrC2I3AAAAChUSUQAAALkwDEOSNHLkSFWqVEkNGjTQwIEDtX79epteUbcrKytL69evV+vWra3L2rRpo/Xr19vMPwUAAHA/Yo4oAACAXPj4+KhYsWIqUqSIdVnp0qVlGIaio6MVGBgoHx8fxcXF2WwXFxcnHx+fPOvdvXu3Ll++rClTptgsz8rK0v79+1WnTp383A0AAIBChUQUAABALqpVq6YtW7YoJSVFbm5ukqRz587JYrHIz89PklSlShX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     },
     "metadata": {}
    }
   ],
   "source": "# Week 1 - Cell 1: Imports, molecules, and geometry visualization\nfrom qiskit_nature.second_q.drivers import PySCFDriver\nfrom qiskit_nature.second_q.transformers import ActiveSpaceTransformer, FreezeCoreTransformer\nfrom qiskit_nature.second_q.mappers import JordanWignerMapper, ParityMapper, BravyiKitaevMapper\nfrom qiskit_nature.units import DistanceUnit\nfrom qiskit.quantum_info import SparsePauliOp\nimport numpy as np\n\nMOLECULES = {\n    \"H2\":  \"H 0.0 0.0 0.0; H 0.0 0.0 0.735\",\n    \"LiH\": \"Li 0.0 0.0 0.0; H 0.0 0.0 1.6\",\n    \"BeH2\": \"Be 0.0 0.0 0.0; H 0.0 0.0 1.326; H 0.0 0.0 -1.326\"\n}\n\ndef build_problem(atom_str, basis=\"sto-3g\", charge=0, spin=0):\n    # Create an ElectronicStructureProblem via PySCF\n    driver = PySCFDriver(atom=atom_str, basis=basis, charge=charge,\n                         spin=spin, unit=DistanceUnit.ANGSTROM)\n    return driver.run()\n\nproblem_full = build_problem(MOLECULES[\"LiH\"])\n\nprint(\"=\" * 60)\nprint(\"FULL LiH PROBLEM (STO-3G)\")\nprint(\"=\" * 60)\nprint(f\"Particles (alpha, beta) : {problem_full.num_particles}\")\nprint(f\"Spatial orbitals        : {problem_full.num_spatial_orbitals}\")\nprint(f\"Qubits (Jordan-Wigner)  : {2 * problem_full.num_spatial_orbitals}\")\n\n# ----- Molecular geometry diagram -----\nfig, axes = plt.subplots(1, 3, figsize=(12, 3.8))\nfig.suptitle(\"Course Molecules – Geometry (Angstrom)\", fontsize=14, fontweight=\"bold\")\n\n# H2\nax = axes[0]\nax.scatter([0, 0.735], [0, 0], s=600, c=[\"#4C72B0\", \"#4C72B0\"], zorder=5, edgecolors=\"k\")\nax.plot([0, 0.735], [0, 0], \"k-\", lw=3, zorder=1)\nax.text(0, 0.18, \"H\", ha=\"center\", fontsize=14, fontweight=\"bold\")\nax.text(0.735, 0.18, \"H\", ha=\"center\", fontsize=14, fontweight=\"bold\")\nax.text(0.367, -0.25, \"0.735 A\", ha=\"center\", fontsize=10, color=\"#555\")\nax.set_xlim(-0.4, 1.15); ax.set_ylim(-0.5, 0.5)\nax.set_aspect(\"equal\"); ax.axis(\"off\"); ax.set_title(\"H$_2$\")\n\n# LiH\nax = axes[1]\nax.scatter([0, 1.6], [0, 0], s=[900, 500], c=[\"#DD8452\", \"#4C72B0\"], zorder=5, edgecolors=\"k\")\nax.plot([0, 1.6], [0, 0], \"k-\", lw=3, zorder=1)\nax.text(0, 0.22, \"Li\", ha=\"center\", fontsize=14, fontweight=\"bold\")\nax.text(1.6, 0.22, \"H\", ha=\"center\", fontsize=14, fontweight=\"bold\")\nax.text(0.8, -0.28, \"1.60 A\", ha=\"center\", fontsize=10, color=\"#555\")\nax.set_xlim(-0.5, 2.1); ax.set_ylim(-0.55, 0.55)\nax.set_aspect(\"equal\"); ax.axis(\"off\"); ax.set_title(\"LiH\")\n\n# BeH2\nax = axes[2]\nax.scatter([0, 1.326, -1.326], [0, 0, 0], s=[850, 500, 500],\n           c=[\"#55A868\", \"#4C72B0\", \"#4C72B0\"], zorder=5, edgecolors=\"k\")\nax.plot([-1.326, 1.326], [0, 0], \"k-\", lw=3, zorder=1)\nax.text(0, 0.22, \"Be\", ha=\"center\", fontsize=14, fontweight=\"bold\")\nax.text(1.326, 0.22, \"H\", ha=\"center\", fontsize=13, fontweight=\"bold\")\nax.text(-1.326, 0.22, \"H\", ha=\"center\", fontsize=13, fontweight=\"bold\")\nax.text(0.66, -0.28, \"1.33 A\", ha=\"center\", fontsize=10, color=\"#555\")\nax.set_xlim(-1.9, 1.9); ax.set_ylim(-0.55, 0.55)\nax.set_aspect(\"equal\"); ax.axis(\"off\"); ax.set_title(\"BeH$_2$\")\n\nplt.tight_layout()\nplt.show()\n"
  },
  {
   "cell_type": "markdown",
   "id": "4d3cd4b7",
   "metadata": {
    "id": "4d3cd4b7"
   },
   "source": "### 1.2 Active-Space Reduction – Concept Diagram + Code\n"
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a49a1c52",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 706
    },
    "id": "a49a1c52",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1786421993552,
     "user_tz": -180,
     "elapsed": 498,
     "user": {
      "displayName": "Joseph Volkan ÖZCAN",
      "userId": "11389530967736397480"
     }
    },
    "outputId": "9bd3c731-ba31-4ab3-94ba-49453bf1815b"
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "============================================================\n",
      "ACTIVE-SPACE REDUCED PROBLEM (2e, 2o)\n",
      "============================================================\n",
      "Particles (alpha, beta)    : (1, 1)\n",
      "Spatial orbitals           : 2\n",
      "Qubits under Jordan-Wigner : 4\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 800x550 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\n",
      "Interpretation: only the chemically relevant frontier orbitals enter the quantum algorithm.\n",
      "This is the main reason NISQ quantum chemistry is feasible for small molecules.\n"
     ]
    }
   ],
   "source": "# Week 1 - Cell 2: Active space reduction + orbital energy diagram\n\nas_transformer = ActiveSpaceTransformer(num_electrons=2, num_spatial_orbitals=2)\nproblem_reduced = as_transformer.transform(problem_full)\n\nprint(\"=\" * 60)\nprint(\"ACTIVE-SPACE REDUCED PROBLEM (2e, 2o)\")\nprint(\"=\" * 60)\nprint(f\"Particles (alpha, beta)    : {problem_reduced.num_particles}\")\nprint(f\"Spatial orbitals           : {problem_reduced.num_spatial_orbitals}\")\nprint(f\"Qubits under Jordan-Wigner : {2 * problem_reduced.num_spatial_orbitals}\")\n\n# ----- Conceptual orbital diagram -----\nfig, ax = plt.subplots(figsize=(8, 5.5))\nax.set_title(\"Active-Space Concept (LiH-like orbital picture)\", fontweight=\"bold\")\n\n# Approximate orbital energies (illustrative, not exact)\norbitals = [\n    (\"1s (core)\", -2.4, \"frozen\", \"#888888\"),\n    (\"2s\", -0.35, \"active\", \"#4C72B0\"),\n    (\"2p\", 0.05, \"active\", \"#4C72B0\"),\n    (\"3s / virtual\", 0.55, \"virtual\", \"#55A868\"),\n    (\"higher virtual\", 1.1, \"virtual\", \"#55A868\"),\n]\n\nfor i, (label, energy, kind, color) in enumerate(orbitals):\n    y = energy\n    ax.hlines(y, 0.3, 1.7, colors=color, lw=4, zorder=3)\n    ax.text(1.85, y, label, va=\"center\", fontsize=11)\n    if kind == \"active\":\n        ax.add_patch(Rectangle((0.25, y-0.12), 1.55, 0.24,\n                               facecolor=\"#4C72B0\", alpha=0.15, zorder=1))\n\n# Electrons\nax.scatter([0.7, 1.3], [-0.35, -0.35], s=120, c=\"k\", zorder=5, marker=\"o\")\nax.scatter([0.7], [-2.4], s=120, c=\"k\", zorder=5, marker=\"o\")  # core pair simplified\n\nax.axhspan(-0.55, 0.25, alpha=0.08, color=\"#4C72B0\", label=\"Active space (kept)\")\nax.axhspan(-2.8, -1.8, alpha=0.08, color=\"#888888\", label=\"Frozen core\")\nax.axhspan(0.35, 1.4, alpha=0.08, color=\"#55A868\", label=\"Virtual (discarded)\")\n\nax.set_xlim(0, 3.6)\nax.set_ylim(-2.9, 1.5)\nax.set_ylabel(\"Relative orbital energy (illustrative)\")\nax.set_xticks([])\nax.legend(loc=\"lower right\", framealpha=0.95)\nax.spines[\"top\"].set_visible(False)\nax.spines[\"right\"].set_visible(False)\nax.spines[\"bottom\"].set_visible(False)\nplt.tight_layout()\nplt.show()\n\nprint(\"\\nInterpretation: only the chemically relevant frontier orbitals enter the quantum algorithm.\")\nprint(\"This is the main reason NISQ quantum chemistry is feasible for small molecules.\")\n"
  },
  {
   "cell_type": "markdown",
   "id": "35d9dc4e",
   "metadata": {
    "id": "35d9dc4e"
   },
   "source": "### 1.3 Fermion-to-Qubit Mappings – Comparison Chart\n"
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "38aab97f",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 497
    },
    "id": "38aab97f",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1786421994652,
     "user_tz": -180,
     "elapsed": 840,
     "user": {
      "displayName": "Joseph Volkan ÖZCAN",
      "userId": "11389530967736397480"
     }
    },
    "outputId": "155ee191-74ef-4b31-82b3-989ed93234d4"
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Jordan-Wigner       qubits= 4  Pauli terms= 27\n",
      "Parity              qubits= 2  Pauli terms=  9\n",
      "Bravyi-Kitaev       qubits= 4  Pauli terms= 27\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\n",
      "Parity mapping often wins for small molecules because of the 2-qubit reduction.\n"
     ]
    }
   ],
   "source": "# Week 1 - Cell 3: Mapper comparison + bar chart\n\nmappers = {\n    \"Jordan-Wigner\": JordanWignerMapper(),\n    \"Parity\":        ParityMapper(num_particles=problem_reduced.num_particles),\n    \"Bravyi-Kitaev\": BravyiKitaevMapper()\n}\n\nnames, n_qubits, n_terms = [], [], []\nqubit_ops = {}\nfor name, mapper in mappers.items():\n    op = mapper.map(problem_reduced.hamiltonian.second_q_op())\n    qubit_ops[name] = op\n    names.append(name)\n    n_qubits.append(op.num_qubits)\n    n_terms.append(len(op))\n    print(f\"{name:<18}  qubits={op.num_qubits:2d}  Pauli terms={len(op):3d}\")\n\nfig, axes = plt.subplots(1, 2, figsize=(10, 4))\nfig.suptitle(\"Mapper Impact on Resource Requirements (LiH 2e/2o)\", fontweight=\"bold\")\n\ncolors = [\"#4C72B0\", \"#DD8452\", \"#55A868\"]\naxes[0].bar(names, n_qubits, color=colors, edgecolor=\"k\", width=0.55)\naxes[0].set_ylabel(\"Number of qubits\")\naxes[0].set_title(\"Qubit count\")\nfor i, v in enumerate(n_qubits):\n    axes[0].text(i, v + 0.08, str(v), ha=\"center\", fontweight=\"bold\")\n\naxes[1].bar(names, n_terms, color=colors, edgecolor=\"k\", width=0.55)\naxes[1].set_ylabel(\"Number of Pauli terms\")\naxes[1].set_title(\"Hamiltonian complexity\")\nfor i, v in enumerate(n_terms):\n    axes[1].text(i, v + 0.3, str(v), ha=\"center\", fontweight=\"bold\")\n\nplt.tight_layout()\nplt.show()\n\nprint(\"\\nParity mapping often wins for small molecules because of the 2-qubit reduction.\")\n"
  },
  {
   "cell_type": "markdown",
   "id": "bed529e6",
   "metadata": {
    "id": "bed529e6"
   },
   "source": "### 1.4 Hardware Topology Awareness – Heavy-Hex Lattice Diagram\n"
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4c961bd8",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 570
    },
    "id": "4c961bd8",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1786421995756,
     "user_tz": -180,
     "elapsed": 798,
     "user": {
      "displayName": "Joseph Volkan ÖZCAN",
      "userId": "11389530967736397480"
     }
    },
    "outputId": "50774519-c0f3-4d8a-f9c2-4cbdd587f8d9"
   },
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 900x550 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "In production you query the real backend coupling map and transpile with optimization_level=3.\n"
     ]
    }
   ],
   "source": "# Week 1 - Cell 4: Heavy-hex topology visualization (educational)\n\nfrom qiskit.transpiler import CouplingMap\nimport networkx as nx\n\n# Illustrative heavy-hex fragment inspired by IBM architectures\n# (Condor is a much larger instance of the same lattice family)\nedges = [\n    (0,1), (1,2), (2,3), (3,4), (4,5),\n    (1,6), (3,7), (5,8),\n    (6,9), (7,10), (8,11),\n    (9,10), (10,11),\n    (6,12), (8,13),\n    (12,14), (13,15), (14,15)\n]\ncm = CouplingMap(edges)\nG = nx.Graph()\nG.add_edges_from(edges)\n\n# Layout that roughly resembles a heavy-hex fragment\npos = {\n    0:(0,2), 1:(1,2), 2:(2,2), 3:(3,2), 4:(4,2), 5:(5,2),\n    6:(1,1), 7:(3,1), 8:(5,1),\n    9:(1,0), 10:(3,0), 11:(5,0),\n    12:(0.5,-1), 13:(5.5,-1),\n    14:(1.5,-2), 15:(4.5,-2)\n}\n\nfig, ax = plt.subplots(figsize=(9, 5.5))\nnx.draw_networkx_nodes(G, pos, node_color=\"#4C72B0\", node_size=700,\n                       edgecolors=\"k\", linewidths=1.5, ax=ax)\nnx.draw_networkx_edges(G, pos, width=2.2, edge_color=\"#555\", ax=ax)\nnx.draw_networkx_labels(G, pos, font_color=\"white\", font_weight=\"bold\", font_size=10, ax=ax)\nax.set_title(\"Illustrative Heavy-Hex Coupling Map\\n(IBM Condor / Eagle-family style fragment)\", fontweight=\"bold\")\nax.axis(\"off\")\nax.text(0.02, 0.02,\n        \"Real Condor has 1,121 qubits arranged in an extended heavy-hex lattice.\\n\"\n        \"Transpilation must respect connectivity → SWAP overhead grows with distance.\",\n        transform=ax.transAxes, fontsize=9, va=\"bottom\",\n        bbox=dict(boxstyle=\"round\", facecolor=\"wheat\", alpha=0.85))\nplt.tight_layout()\nplt.show()\n\nprint(\"In production you query the real backend coupling map and transpile with optimization_level=3.\")\n"
  },
  {
   "cell_type": "markdown",
   "id": "defe64a8",
   "metadata": {
    "id": "defe64a8"
   },
   "source": "### Week 1 – Summary & Checkpoint\n- You can generate molecular Hamiltonians, reduce them with active-space techniques, and map them to qubits.\n- Qubit count and Pauli-term count are the primary cost drivers for VQE on superconducting hardware.\n- Heavy-hex connectivity forces careful transpilation on Condor-class devices.\n"
  },
  {
   "cell_type": "markdown",
   "id": "d88067bf",
   "metadata": {
    "id": "d88067bf"
   },
   "source": "---\n# Week 2: Ground & Excited States via Variational Solvers\n\n### Theoretical Content\n- Variational Quantum Eigensolver (VQE) architecture\n- Unitary Coupled Cluster (UCCSD) Ansatz\n- Optimization landscapes and convergence\n- Quantum Equation of Motion (qEOM) for excited states\n\n### Hands-on Goals\n1. Compute ground-state energies of H₂ and LiH with UCCSD-VQE\n2. Visualize the VQE workflow and the ansatz circuit\n3. Compute excited states with qEOM\n4. Understand the path to large hardware\n"
  },
  {
   "cell_type": "markdown",
   "id": "683953b1",
   "metadata": {
    "id": "683953b1"
   },
   "source": "### 2.0 VQE Workflow Diagram\n"
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a939f374",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 484
    },
    "id": "a939f374",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1786421996503,
     "user_tz": -180,
     "elapsed": 740,
     "user": {
      "displayName": "Joseph Volkan ÖZCAN",
      "userId": "11389530967736397480"
     }
    },
    "outputId": "99dcacb0-ee28-433e-e46c-d0e638eb9de0"
   },
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 1100x480 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {}
    }
   ],
   "source": "# Week 2 - Visual: VQE hybrid loop diagram\n\nfig, ax = plt.subplots(figsize=(11, 4.8))\nax.set_xlim(0, 11)\nax.set_ylim(0, 5)\nax.axis(\"off\")\nax.set_title(\"Variational Quantum Eigensolver (VQE) – Hybrid Loop\", fontsize=14, fontweight=\"bold\", pad=12)\n\ndef box(x, y, w, h, text, color, ax):\n    p = FancyBboxPatch((x, y), w, h, boxstyle=\"round,pad=0.05,rounding_size=0.15\",\n                       facecolor=color, edgecolor=\"k\", linewidth=1.5, zorder=2)\n    ax.add_patch(p)\n    ax.text(x + w/2, y + h/2, text, ha=\"center\", va=\"center\", fontsize=10,\n            fontweight=\"bold\", wrap=True, zorder=3)\n\n# Boxes\nbox(0.3, 3.2, 2.4, 1.2, \"Classical\\nOptimizer\\n(SLSQP / COBYLA)\", \"#FFD966\", ax)\nbox(3.5, 3.2, 2.6, 1.2, \"Parameterized\\nAnsatz U(theta)\\n(UCCSD + HF)\", \"#9FC5E8\", ax)\nbox(6.9, 3.2, 2.4, 1.2, \"Quantum\\nHardware /\\nSimulator\", \"#B6D7A8\", ax)\nbox(3.5, 0.6, 2.6, 1.2, \"Estimate\\n<H>(theta)\", \"#D5A6BD\", ax)\nbox(0.3, 0.6, 2.4, 1.2, \"Update theta\\nuntil convergence\", \"#F9CB9C\", ax)\n\n# Arrows\ndef arrow(x1, y1, x2, y2):\n    ax.annotate(\"\", xy=(x2, y2), xytext=(x1, y1),\n                arrowprops=dict(arrowstyle=\"->\", color=\"#333\", lw=2))\n\narrow(2.7, 3.8, 3.5, 3.8)   # optimizer -> ansatz\narrow(6.1, 3.8, 6.9, 3.8)   # ansatz -> QPU\narrow(8.1, 3.2, 8.1, 1.8)   # QPU down\narrow(8.1, 1.8, 6.1, 1.2)   # to estimate\narrow(3.5, 1.2, 2.7, 1.2)   # estimate -> update\narrow(1.5, 1.8, 1.5, 3.2)   # update -> optimizer\n\nax.text(5.5, 4.7, \"theta parameters\", ha=\"center\", fontsize=9, style=\"italic\", color=\"#444\")\nax.text(9.6, 2.5, \"measurement\\nresults\", ha=\"center\", fontsize=9, style=\"italic\", color=\"#444\")\nax.text(5.5, 0.25, \"energy estimate feeds classical optimizer\", ha=\"center\", fontsize=9, style=\"italic\", color=\"#444\")\n\nplt.tight_layout()\nplt.show()\n"
  },
  {
   "cell_type": "markdown",
   "id": "14bbb23e",
   "metadata": {
    "id": "14bbb23e"
   },
   "source": "### 2.1 Complete VQE Pipeline for H₂ + Circuit Drawing\n"
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "67a9c135",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 258
    },
    "id": "67a9c135",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1786422002453,
     "user_tz": -180,
     "elapsed": 5795,
     "user": {
      "displayName": "Joseph Volkan ÖZCAN",
      "userId": "11389530967736397480"
     }
    },
    "outputId": "81fdd7f8-0833-4555-85f3-53cacb23d18c"
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "H2 problem: particles = (1, 1) | spatial orbitals = 2\n",
      "Ansatz qubits: 2 | parameters: 3\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 900x500 with 0 Axes>"
      ]
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "/usr/local/lib/python3.12/dist-packages/scipy/sparse/linalg/_dsolve/linsolve.py:606: SparseEfficiencyWarning: splu converted its input to CSC format\n",
      "  return splu(A).solve\n",
      "/usr/local/lib/python3.12/dist-packages/scipy/sparse/linalg/_matfuncs.py:707: SparseEfficiencyWarning: spsolve is more efficient when sparse b is in the CSC matrix format\n",
      "  return spsolve(Q, P)\n"
     ]
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "============================================================\n",
      "H2 GROUND-STATE VQE RESULT\n",
      "============================================================\n",
      "Total energy     : -1.13730604 Ha\n",
      "Electronic energy: -1.85727503 Ha\n",
      "Reference (FCI/STO-3G) approx -1.137 Ha electronic\n"
     ]
    }
   ],
   "source": "# Week 2 - Cell 1: Full VQE for H2 + ansatz visualization\n\nfrom qiskit_nature.second_q.circuit.library import HartreeFock, UCCSD\nfrom qiskit_nature.second_q.algorithms import GroundStateEigensolver\nfrom qiskit_algorithms import VQE\nfrom qiskit_algorithms.optimizers import SLSQP\nfrom qiskit.primitives import StatevectorEstimator\n\nproblem_h2 = build_problem(MOLECULES[\"H2\"])\nprint(\"H2 problem: particles =\", problem_h2.num_particles,\n      \"| spatial orbitals =\", problem_h2.num_spatial_orbitals)\n\nmapper = ParityMapper(num_particles=problem_h2.num_particles)\nhf_state = HartreeFock(problem_h2.num_spatial_orbitals, problem_h2.num_particles, mapper)\nansatz = UCCSD(problem_h2.num_spatial_orbitals, problem_h2.num_particles, mapper,\n               initial_state=hf_state)\n\nprint(f\"Ansatz qubits: {ansatz.num_qubits} | parameters: {ansatz.num_parameters}\")\n\n# Draw the ansatz circuit (decomposed enough to be readable)\nsafe_circuit_draw(ansatz.decompose(), title=\"UCCSD Ansatz for H2 (Parity mapping)\", fold=40)\n\n# Run VQE\nestimator = StatevectorEstimator()\nvqe = VQE(estimator, ansatz, SLSQP(maxiter=250))\nvqe.initial_point = np.zeros(ansatz.num_parameters)\nsolver = GroundStateEigensolver(mapper, vqe)\nresult_h2 = solver.solve(problem_h2)\n\nprint(\"=\" * 60)\nprint(\"H2 GROUND-STATE VQE RESULT\")\nprint(\"=\" * 60)\nprint(f\"Total energy     : {result_h2.total_energies[0]:.8f} Ha\")\nprint(f\"Electronic energy: {result_h2.electronic_energies[0]:.8f} Ha\")\nprint(\"Reference (FCI/STO-3G) approx -1.137 Ha electronic\")\n"
  },
  {
   "cell_type": "markdown",
   "id": "98b82b3a",
   "metadata": {
    "id": "98b82b3a"
   },
   "source": "### 2.2 Potential Energy Surface (PES) Scan for H₂\n"
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "5b5fec09",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 540
    },
    "id": "5b5fec09",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1786422003706,
     "user_tz": -180,
     "elapsed": 1044,
     "user": {
      "displayName": "Joseph Volkan ÖZCAN",
      "userId": "11389530967736397480"
     }
    },
    "outputId": "6b30e215-608d-421c-e269-a161fef6b4c1"
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Scanning H2 PES (this may take ~20-40 s)...\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 900x520 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {}
    }
   ],
   "source": "# Week 2 - Visual: H2 potential energy surface (classical reference + VQE points)\n\nfrom qiskit_nature.second_q.drivers import PySCFDriver\n\ndistances = np.linspace(0.4, 2.5, 18)\nenergies_hf = []\nenergies_fci = []\n\nprint(\"Scanning H2 PES (this may take ~20-40 s)...\")\nfor d in distances:\n    driver = PySCFDriver(atom=f\"H 0 0 0; H 0 0 {d}\", basis=\"sto-3g\",\n                         unit=DistanceUnit.ANGSTROM)\n    problem = driver.run()\n    # Nuclear repulsion is included in total energy later; we store electronic + nuclear via driver\n    # For simplicity we recompute total energy via a quick classical solver path\n    from pyscf import gto, scf, fci\n    mol = gto.M(atom=f\"H 0 0 0; H 0 0 {d}\", basis=\"sto3g\", unit=\"Angstrom\", verbose=0)\n    mf = scf.RHF(mol).run()\n    energies_hf.append(mf.e_tot)\n    cisolver = fci.FCI(mol, mf.mo_coeff)\n    e_fci, _ = cisolver.kernel()\n    energies_fci.append(e_fci + mol.energy_nuc())\n\n# VQE result at equilibrium (from previous cell)\nvqe_dist = 0.735\nvqe_e = result_h2.total_energies[0]\n\nfig, ax = plt.subplots(figsize=(9, 5.2))\nax.plot(distances, energies_hf, \"o--\", label=\"Hartree-Fock\", color=\"#DD8452\", markersize=5)\nax.plot(distances, energies_fci, \"s-\", label=\"FCI (exact in STO-3G)\", color=\"#4C72B0\", markersize=5)\nax.scatter([vqe_dist], [vqe_e], s=180, c=\"#55A868\", marker=\"*\", zorder=5,\n           label=f\"VQE (UCCSD) @ 0.735 A = {vqe_e:.4f} Ha\", edgecolors=\"k\")\nax.axvline(0.735, color=\"gray\", ls=\":\", alpha=0.7)\nax.set_xlabel(\"H–H distance (Angstrom)\")\nax.set_ylabel(\"Total energy (Hartree)\")\nax.set_title(\"H$_2$ Potential Energy Surface – Classical vs VQE\", fontweight=\"bold\")\nax.legend(loc=\"upper right\")\nax.set_ylim(min(energies_fci)-0.05, max(energies_hf)+0.05)\nplt.tight_layout()\nplt.show()\n"
  },
  {
   "cell_type": "markdown",
   "id": "6c3f1854",
   "metadata": {
    "id": "6c3f1854"
   },
   "source": "### 2.3 VQE for LiH (Active Space) + Energy Comparison Chart\n"
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0152a023",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 489
    },
    "id": "0152a023",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1786422006406,
     "user_tz": -180,
     "elapsed": 2353,
     "user": {
      "displayName": "Joseph Volkan ÖZCAN",
      "userId": "11389530967736397480"
     }
    },
    "outputId": "a8e30a87-b319-407b-a412-6f704646b0c8"
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "============================================================\n",
      "LiH (2e,2o) GROUND-STATE VQE RESULT\n",
      "============================================================\n",
      "Total energy     : -7.86212881 Ha\n",
      "Electronic energy: -8.85433608 Ha\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {}
    }
   ],
   "source": "# Week 2 - Cell 2: LiH active-space VQE + comparison bar\n\nproblem_lih_full = build_problem(MOLECULES[\"LiH\"])\nas_transformer = ActiveSpaceTransformer(num_electrons=2, num_spatial_orbitals=2)\nproblem_lih = as_transformer.transform(problem_lih_full)\n\nmapper_lih = ParityMapper(num_particles=problem_lih.num_particles)\nhf_lih = HartreeFock(problem_lih.num_spatial_orbitals, problem_lih.num_particles, mapper_lih)\nansatz_lih = UCCSD(problem_lih.num_spatial_orbitals, problem_lih.num_particles, mapper_lih,\n                   initial_state=hf_lih)\n\nvqe_lih = VQE(StatevectorEstimator(), ansatz_lih, SLSQP(maxiter=300))\nvqe_lih.initial_point = np.zeros(ansatz_lih.num_parameters)\nsolver_lih = GroundStateEigensolver(mapper_lih, vqe_lih)\nresult_lih = solver_lih.solve(problem_lih)\n\nprint(\"=\" * 60)\nprint(\"LiH (2e,2o) GROUND-STATE VQE RESULT\")\nprint(\"=\" * 60)\nprint(f\"Total energy     : {result_lih.total_energies[0]:.8f} Ha\")\nprint(f\"Electronic energy: {result_lih.electronic_energies[0]:.8f} Ha\")\n\n# Comparison chart\nlabels = [\"H2 VQE total\", \"LiH VQE total\"]\nvals = [result_h2.total_energies[0], result_lih.total_energies[0]]\nfig, ax = plt.subplots(figsize=(7, 4))\nbars = ax.bar(labels, vals, color=[\"#4C72B0\", \"#DD8452\"], edgecolor=\"k\", width=0.45)\nax.set_ylabel(\"Total energy (Ha)\")\nax.set_title(\"Ground-State Energies from UCCSD-VQE\", fontweight=\"bold\")\nfor b, v in zip(bars, vals):\n    ax.text(b.get_x() + b.get_width()/2, v + 0.01 if v > 0 else v - 0.03,\n            f\"{v:.5f}\", ha=\"center\", fontweight=\"bold\", fontsize=10)\nax.axhline(0, color=\"k\", lw=0.8)\nplt.tight_layout()\nplt.show()\n"
  },
  {
   "cell_type": "markdown",
   "id": "a6cdf538",
   "metadata": {
    "id": "a6cdf538"
   },
   "source": "### 2.4 Excited States with qEOM\n"
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a8656cb6",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "id": "a8656cb6",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1786422007955,
     "user_tz": -180,
     "elapsed": 1153,
     "user": {
      "displayName": "Joseph Volkan ÖZCAN",
      "userId": "11389530967736397480"
     }
    },
    "outputId": "42e390c4-a06b-4505-a013-374c965e0200"
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "============================================================\n",
      "H2 EXCITED-STATE RESULTS (qEOM)\n",
      "============================================================\n",
      "=== GROUND STATE ENERGY ===\n",
      " \n",
      "* Electronic ground state energy (Hartree): -1.857275030145\n",
      "  - computed part:      -1.857275030145\n",
      "~ Nuclear repulsion energy (Hartree): 0.719968994449\n",
      "> Total ground state energy (Hartree): -1.137306035696\n",
      " \n",
      "=== EXCITED STATE ENERGIES ===\n",
      " \n",
      "  1: \n",
      "* Electronic excited state energy (Hartree): -1.244586749357\n",
      "> Total excited state energy (Hartree): -0.524617754908\n",
      "  2: \n",
      "* Electronic excited state energy (Hartree): -0.882724349759\n",
      "> Total excited state energy (Hartree): -0.16275535531\n",
      "  3: \n",
      "* Electronic excited state energy (Hartree): -0.224913452353\n",
      "> Total excited state energy (Hartree): 0.495055542096\n",
      " \n",
      "=== MEASURED OBSERVABLES ===\n",
      " \n",
      "  0:  # Particles: 0.000 S: 0.000 S^2: 0.000 M: 0.000\n",
      "  1:  # Particles: 0.000 S: 0.000 S^2: 0.000 M: 0.000\n",
      "  2:  # Particles: 0.000 S: 0.000 S^2: 0.000 M: 0.000\n",
      "  3:  # Particles: 0.000 S: 0.000 S^2: 0.000 M: 0.000\n",
      " \n",
      "=== DIPOLE MOMENTS ===\n",
      " \n",
      "~ Nuclear dipole moment (a.u.): [0.0  0.0  1.3889487]\n",
      " \n",
      "  0: \n",
      "  * Electronic dipole moment (a.u.): [0.0  0.0  0.0]\n",
      "    - computed part:      [0.0  0.0  0.0]\n",
      "  > Dipole moment (a.u.): [0.0  0.0  1.3889487]  Total: 1.3889487\n",
      "                 (debye): [0.0  0.0  3.530355123354]  Total: 3.530355123354\n",
      " \n",
      "  1: \n",
      "  * Electronic dipole moment (a.u.): [0.0  0.0  0.0]\n",
      "    - computed part:      [0.0  0.0  0.0]\n",
      "  > Dipole moment (a.u.): [0.0  0.0  1.3889487]  Total: 1.3889487\n",
      "                 (debye): [0.0  0.0  3.530355123354]  Total: 3.530355123354\n",
      " \n",
      "  2: \n",
      "  * Electronic dipole moment (a.u.): [0.0  0.0  0.0]\n",
      "    - computed part:      [0.0  0.0  0.0]\n",
      "  > Dipole moment (a.u.): [0.0  0.0  1.3889487]  Total: 1.3889487\n",
      "                 (debye): [0.0  0.0  3.530355123354]  Total: 3.530355123354\n",
      " \n",
      "  3: \n",
      "  * Electronic dipole moment (a.u.): [0.0  0.0  0.0]\n",
      "    - computed part:      [0.0  0.0  0.0]\n",
      "  > Dipole moment (a.u.): [0.0  0.0  1.3889487]  Total: 1.3889487\n",
      "                 (debye): [0.0  0.0  3.530355123354]  Total: 3.530355123354\n",
      " \n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {}
    }
   ],
   "source": "# Week 2 - Cell 3: qEOM for excited states (H2)\n\nfrom qiskit_nature.second_q.algorithms import QEOM\n\nqeom = QEOM(solver, estimator, excitations=\"sd\")\nexcited = qeom.solve(problem_h2)\n\nprint(\"=\" * 60)\nprint(\"H2 EXCITED-STATE RESULTS (qEOM)\")\nprint(\"=\" * 60)\nprint(excited)\n\n# Simple energy-level diagram if excitation data is present\ntry:\n    gs = result_h2.total_energies[0]\n    # qEOM result structure can vary by version; attempt common attributes\n    exc = None\n    if hasattr(excited, \"computed_energies\"):\n        exc = np.array(excited.computed_energies).real\n    elif hasattr(excited, \"excitation_energies\"):\n        exc = np.array(excited.excitation_energies).real + gs\n\n    if exc is not None and len(exc) > 0:\n        levels = np.concatenate(([gs], exc[:4]))\n        fig, ax = plt.subplots(figsize=(5, 5))\n        for i, e in enumerate(levels):\n            ax.hlines(e, 0.3, 1.7, colors=\"#4C72B0\" if i == 0 else \"#DD8452\", lw=3)\n            label = \"Ground\" if i == 0 else f\"Exc. {i}\"\n            ax.text(1.85, e, f\"{label}: {e:.4f} Ha\", va=\"center\", fontsize=10)\n        ax.set_xlim(0, 3.5)\n        ax.set_ylabel(\"Energy (Ha)\")\n        ax.set_title(\"H2 Energy Levels (VQE + qEOM)\", fontweight=\"bold\")\n        ax.set_xticks([])\n        ax.spines[\"top\"].set_visible(False)\n        ax.spines[\"right\"].set_visible(False)\n        ax.spines[\"bottom\"].set_visible(False)\n        plt.tight_layout()\n        plt.show()\nexcept Exception as e:\n    print(\"Energy-level plot skipped (result structure variation):\", type(e).__name__)\n"
  },
  {
   "cell_type": "markdown",
   "id": "c7dbd363",
   "metadata": {
    "id": "c7dbd363"
   },
   "source": "### 2.5 Path to Hardware (>1000 qubits)\n\n```python\n# Example skeleton for IBM Quantum Runtime (requires token)\nfrom qiskit_ibm_runtime import QiskitRuntimeService, EstimatorV2, Session\n\nservice = QiskitRuntimeService(channel=\"ibm_quantum\", token=\"YOUR_TOKEN\")\nbackend = service.least_busy(operational=True, simulator=False, min_num_qubits=100)\n\nwith Session(backend=backend) as session:\n    estimator = EstimatorV2(session=session)\n    vqe_hw = VQE(estimator, ansatz, optimizer)\n    ...\n```\n\n**Practical notes**\n- UCCSD depth grows rapidly → adaptive / hardware-efficient ansatze become attractive.\n- Always start from the Hartree-Fock state.\n- Error mitigation is mandatory beyond ~10–15 qubits on current devices.\n"
  },
  {
   "cell_type": "markdown",
   "id": "c3f87375",
   "metadata": {
    "id": "c3f87375"
   },
   "source": "---\n# Week 3: Quantum Machine Learning (QML) for Advanced Matter\n\n### Theoretical Content\n- Data encoding (Angle vs Amplitude)\n- Quantum Kernel Methods\n- Variational Quantum Classifiers / Quantum Neural Networks\n- Application to material phase classification and formation-energy prediction\n"
  },
  {
   "cell_type": "markdown",
   "id": "ff38c927",
   "metadata": {
    "id": "ff38c927"
   },
   "source": "### 3.1 Quantum Kernel + QSVC – Feature Map & Kernel Heatmap\n"
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "25ed3e85",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "id": "25ed3e85",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1786422131195,
     "user_tz": -180,
     "elapsed": 123045,
     "user": {
      "displayName": "Joseph Volkan ÖZCAN",
      "userId": "11389530967736397480"
     }
    },
    "outputId": "f0058dac-725d-4cec-ce94-6bfd8d761e28"
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "/tmp/ipykernel_493/4081087737.py:22: DeprecationWarning: The class ``qiskit.circuit.library.data_preparation._zz_feature_map.ZZFeatureMap`` is deprecated as of Qiskit 2.1. It will be removed in Qiskit 3.0. Use the zz_feature_map function as a replacement. Note that this will no longer return a BlueprintCircuit, but just a plain QuantumCircuit.\n",
      "  feature_map = ZZFeatureMap(feature_dimension=4, reps=2, entanglement=\"full\")\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 900x500 with 0 Axes>"
      ]
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "============================================================\n",
      "QSVC test accuracy: 0.7111\n",
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0      0.727     0.696     0.711        23\n",
      "           1      0.696     0.727     0.711        22\n",
      "\n",
      "    accuracy                          0.711        45\n",
      "   macro avg      0.711     0.711     0.711        45\n",
      "weighted avg      0.712     0.711     0.711        45\n",
      "\n",
      "Classical RBF-SVM accuracy: 0.8889\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 1100x450 with 3 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 600x380 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {}
    }
   ],
   "source": "# Week 3 - Cell 1: QSVC + rich visualizations\n\nfrom sklearn.datasets import make_classification\nfrom sklearn.model_selection import train_test_split\nfrom sklearn.preprocessing import MinMaxScaler\nfrom sklearn.svm import SVC\nfrom sklearn.metrics import accuracy_score, classification_report, ConfusionMatrixDisplay\n\nfrom qiskit.circuit.library import ZZFeatureMap\nfrom qiskit_machine_learning.kernels import FidelityQuantumKernel\nfrom qiskit_machine_learning.algorithms import QSVC\n\nX, y = make_classification(n_samples=150, n_features=4, n_informative=3,\n                           n_redundant=1, n_classes=2, class_sep=1.2, random_state=42)\nX_train, X_test, y_train, y_test = train_test_split(\n    X, y, test_size=0.30, random_state=42, stratify=y)\n\nscaler = MinMaxScaler(feature_range=(0, np.pi))\nX_train_sc = scaler.fit_transform(X_train)\nX_test_sc  = scaler.transform(X_test)\n\nfeature_map = ZZFeatureMap(feature_dimension=4, reps=2, entanglement=\"full\")\nquantum_kernel = FidelityQuantumKernel(feature_map=feature_map)\n\n# Draw feature map\nsafe_circuit_draw(feature_map.decompose(), title=\"ZZFeatureMap (Angle-style encoding + entanglement)\", fold=50)\n\n# Train QSVC\nqsvc = QSVC(quantum_kernel=quantum_kernel)\nqsvc.fit(X_train_sc, y_train)\ny_pred = qsvc.predict(X_test_sc)\nacc = accuracy_score(y_test, y_pred)\n\nprint(\"=\" * 60)\nprint(f\"QSVC test accuracy: {acc:.4f}\")\nprint(classification_report(y_test, y_pred, digits=3))\n\nsvc_classical = SVC(kernel=\"rbf\")\nsvc_classical.fit(X_train_sc, y_train)\nacc_c = svc_classical.score(X_test_sc, y_test)\nprint(f\"Classical RBF-SVM accuracy: {acc_c:.4f}\")\n\n# Kernel matrix heatmap (subset for speed)\nK = quantum_kernel.evaluate(x_vec=X_train_sc[:40])\nfig, axes = plt.subplots(1, 2, figsize=(11, 4.5))\nsns.heatmap(K, ax=axes[0], cmap=\"viridis\", cbar_kws={\"label\": \"Fidelity\"})\naxes[0].set_title(\"Quantum Kernel Matrix (train subset)\", fontweight=\"bold\")\naxes[0].set_xlabel(\"Sample\"); axes[0].set_ylabel(\"Sample\")\n\nConfusionMatrixDisplay.from_predictions(y_test, y_pred, ax=axes[1], colorbar=False,\n                                        cmap=\"Blues\")\naxes[1].set_title(f\"QSVC Confusion Matrix (acc={acc:.2f})\", fontweight=\"bold\")\nplt.tight_layout()\nplt.show()\n\n# Accuracy comparison\nfig, ax = plt.subplots(figsize=(6, 3.8))\nax.bar([\"Quantum QSVC\", \"Classical RBF-SVM\"], [acc, acc_c],\n       color=[\"#4C72B0\", \"#DD8452\"], edgecolor=\"k\", width=0.5)\nax.set_ylim(0, 1.05)\nax.set_ylabel(\"Test accuracy\")\nax.set_title(\"QML vs Classical SVM on Synthetic Material Data\", fontweight=\"bold\")\nfor i, v in enumerate([acc, acc_c]):\n    ax.text(i, v + 0.02, f\"{v:.3f}\", ha=\"center\", fontweight=\"bold\")\nplt.tight_layout()\nplt.show()\n"
  },
  {
   "cell_type": "markdown",
   "id": "fe2d9277",
   "metadata": {
    "id": "fe2d9277"
   },
   "source": "### 3.2 PennyLane Quantum Neural Network – Architecture & Training Curves\n"
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7aab15ce",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "id": "7aab15ce",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1786422222060,
     "user_tz": -180,
     "elapsed": 90411,
     "user": {
      "displayName": "Joseph Volkan ÖZCAN",
      "userId": "11389530967736397480"
     }
    },
    "outputId": "d4492464-e9c3-4334-dab4-5aca91cc00c1"
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "/tmp/ipykernel_493/3288972965.py:24: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n",
      "  plt.tight_layout()\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Training PennyLane QNN...\n",
      "  Epoch  10 | Train MSE: 0.04914\n",
      "  Epoch  20 | Train MSE: 0.02788\n",
      "  Epoch  30 | Train MSE: 0.01644\n",
      "  Epoch  40 | Train MSE: 0.01494\n",
      "Test MSE: 0.02494\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 1100x420 with 2 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {}
    }
   ],
   "source": "# Week 3 - Cell 2: QNN regression with training curve\n\nimport pennylane as qml\nfrom pennylane import numpy as pnp\n\nn_qubits, n_layers = 4, 2\ndev = qml.device(\"default.qubit\", wires=n_qubits)\n\n@qml.qnode(dev, interface=\"autograd\")\ndef qnn(inputs, weights):\n    # Angle embedding + strongly entangling layers\n    qml.AngleEmbedding(inputs, wires=range(n_qubits), rotation=\"Y\")\n    qml.StronglyEntanglingLayers(weights, wires=range(n_qubits))\n    return qml.expval(qml.PauliZ(0))\n\n# Draw the QNN circuit once\nrng = np.random.default_rng(42)\nweight_shape = qml.StronglyEntanglingLayers.shape(n_layers=n_layers, n_wires=n_qubits)\nw_demo = rng.normal(0, 0.1, weight_shape)\nx_demo = rng.uniform(0, np.pi, n_qubits)\n\nfig, ax = qml.draw_mpl(qnn, decimals=2)(x_demo, w_demo)\nax.set_title(\"PennyLane QNN Circuit (AngleEmbedding + StronglyEntanglingLayers)\", fontweight=\"bold\")\nplt.tight_layout()\nplt.show()\n\n# Synthetic formation-energy style target\nX_reg = rng.uniform(0, np.pi, size=(80, n_qubits))\ny_reg = (0.4*np.sin(X_reg[:,0]) - 0.3*np.cos(X_reg[:,1])\n         + 0.2*X_reg[:,2] + 0.1*np.sin(X_reg[:,3]*2))\ny_reg = (y_reg - y_reg.min()) / (y_reg.max() - y_reg.min())\n\nsplit = 60\nX_train_qnn, X_test_qnn = X_reg[:split], X_reg[split:]\ny_train_qnn, y_test_qnn = y_reg[:split], y_reg[split:]\n\nweights = pnp.array(rng.normal(0, 0.1, weight_shape), requires_grad=True)\nopt = qml.AdamOptimizer(stepsize=0.08)\nepochs = 40\nhistory = []\n\ndef cost(weights, X, y):\n    preds = pnp.array([qnn(x, weights) for x in X])\n    preds_scaled = (preds + 1) / 2\n    return pnp.mean((preds_scaled - y) ** 2)\n\nprint(\"Training PennyLane QNN...\")\nfor epoch in range(epochs):\n    weights, cost_val = opt.step_and_cost(lambda w: cost(w, X_train_qnn, y_train_qnn), weights)\n    history.append(float(cost_val))\n    if (epoch + 1) % 10 == 0:\n        print(f\"  Epoch {epoch+1:3d} | Train MSE: {float(cost_val):.5f}\")\n\ntest_preds = pnp.array([qnn(x, weights) for x in X_test_qnn])\ntest_preds_scaled = (test_preds + 1) / 2\ntest_mse = float(pnp.mean((test_preds_scaled - y_test_qnn) ** 2))\nprint(f\"Test MSE: {test_mse:.5f}\")\n\n# Training curve + prediction scatter\nfig, axes = plt.subplots(1, 2, figsize=(11, 4.2))\naxes[0].plot(history, \"o-\", color=\"#4C72B0\", markersize=4)\naxes[0].set_xlabel(\"Epoch\"); axes[0].set_ylabel(\"Train MSE\")\naxes[0].set_title(\"QNN Training Curve\", fontweight=\"bold\")\n\naxes[1].scatter(y_test_qnn, test_preds_scaled, c=\"#DD8452\", edgecolors=\"k\", s=60, alpha=0.85)\nlims = [0, 1]\naxes[1].plot(lims, lims, \"k--\", alpha=0.6)\naxes[1].set_xlabel(\"True (scaled formation energy)\")\naxes[1].set_ylabel(\"QNN prediction\")\naxes[1].set_title(f\"Test Predictions (MSE={test_mse:.4f})\", fontweight=\"bold\")\naxes[1].set_xlim(lims); axes[1].set_ylim(lims)\nplt.tight_layout()\nplt.show()\n"
  },
  {
   "cell_type": "markdown",
   "id": "7a824565",
   "metadata": {
    "id": "7a824565"
   },
   "source": "### 3.3 Gate-model vs Annealing (D-Wave) Perspective\n\n- **Superconducting gate architectures (Condor / Wukong)** are the natural home for quantum kernels, variational circuits and QNNs.\n- **D-Wave quantum annealing** maps the same tasks onto QUBO problems that fit Chimera / Pegasus / Zephyr topologies.\n\nThe diagrams above show the gate-model path. In the accompanying GitHub repository a QUBO conversion stub for the same classification task is provided for D-Wave Leap users.\n"
  },
  {
   "cell_type": "markdown",
   "id": "7b4b777b",
   "metadata": {
    "id": "7b4b777b"
   },
   "source": "---\n# Week 4: Quantum Dynamics, Error Mitigation & Patent Strategy\n\n### Theoretical Content\n- Quantum time evolution and Trotterization\n- Algorithmic error scaling\n- Zero-Noise Extrapolation (ZNE) and Probabilistic Error Cancellation (PEC)\n- Intellectual-property architectures for quantum-chemical software\n"
  },
  {
   "cell_type": "markdown",
   "id": "faa2c9d9",
   "metadata": {
    "id": "faa2c9d9"
   },
   "source": "### 4.1 Trotterized Time Evolution – Circuit & Conceptual Diagram\n"
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "7358cefb",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 438
    },
    "id": "7358cefb",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1786422223207,
     "user_tz": -180,
     "elapsed": 1046,
     "user": {
      "displayName": "Joseph Volkan ÖZCAN",
      "userId": "11389530967736397480"
     }
    },
    "outputId": "e5637991-949c-4c93-afef-2b2f89b7f8c4"
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Qubits: 2 | Depth after decompose: 32\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 900x500 with 0 Axes>"
      ]
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {}
    }
   ],
   "source": "# Week 4 - Cell 1: Trotter evolution + illustration\n\nfrom qiskit.circuit.library import PauliEvolutionGate\nfrom qiskit.synthesis import SuzukiTrotter\nfrom qiskit import QuantumCircuit\nfrom qiskit.quantum_info import SparsePauliOp\n\nH = SparsePauliOp.from_list([\n    (\"ZZ\", 0.40),\n    (\"XX\", 0.25),\n    (\"YY\", 0.15),\n    (\"ZI\", 0.10),   # single-qubit Z on qubit 0 (padded to 2 qubits)\n    (\"IX\", 0.05),   # single-qubit X on qubit 1 (padded to 2 qubits)\n])\nt, reps = 1.0, 4\nsynthesis = SuzukiTrotter(order=2, reps=reps)\nevo_gate = PauliEvolutionGate(H, time=t, synthesis=synthesis)\n\nqc = QuantumCircuit(H.num_qubits, name=\"TrotterEvolution\")\nqc.append(evo_gate, range(H.num_qubits))\ndecomposed = qc.decompose()\n\nprint(f\"Qubits: {qc.num_qubits} | Depth after decompose: {decomposed.depth()}\")\nsafe_circuit_draw(decomposed, title=\"Second-order Suzuki-Trotter Evolution Circuit\", fold=60)\n\n# Conceptual Trotter error diagram\nfig, ax = plt.subplots(figsize=(8, 4))\nsteps = np.array([1, 2, 4, 8, 16])\n# Illustrative 1/r^2 scaling of Trotter error for 2nd order\nerror = 0.25 / steps**2\nax.plot(steps, error, \"o-\", color=\"#4C72B0\", lw=2, markersize=8)\nax.set_xlabel(\"Number of Trotter steps (r)\")\nax.set_ylabel(\"Illustrative algorithmic error\")\nax.set_title(\"Trotter Error Scaling (2nd-order ~ 1/r$^2$)\", fontweight=\"bold\")\nax.set_xticks(steps)\nfor s, e in zip(steps, error):\n    ax.text(s, e + 0.005, f\"{e:.3f}\", ha=\"center\", fontsize=9)\nplt.tight_layout()\nplt.show()\n"
  },
  {
   "cell_type": "markdown",
   "id": "f094982a",
   "metadata": {
    "id": "f094982a"
   },
   "source": "### 4.2 Noise Model & Zero-Noise Extrapolation (ZNE) – Interactive Concept Plot\n"
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "22588748",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 606
    },
    "id": "22588748",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1786422224261,
     "user_tz": -180,
     "elapsed": 904,
     "user": {
      "displayName": "Joseph Volkan ÖZCAN",
      "userId": "11389530967736397480"
     }
    },
    "outputId": "27883d45-3826-4ce3-e4e7-62eab825c854"
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Noise model constructed:\n",
      "NoiseModel:\n",
      "  Basis gates: ['cx', 'cz', 'ecr', 'id', 'rx', 'ry', 'rz', 'sx', 'x']\n",
      "  Instructions with noise: ['ry', 'sx', 'rz', 'cz', 'ecr', 'rx', 'id', 'cx', 'x']\n",
      "  All-qubits errors: ['rx', 'ry', 'rz', 'id', 'sx', 'x', 'cx', 'ecr', 'cz']\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 850x500 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Lab exercise: replace the synthetic points with real noisy VQE runs at several scale factors.\n"
     ]
    }
   ],
   "source": "# Week 4 - Cell 2: Noise model + ZNE conceptual demonstration\n\nfrom qiskit_aer.noise import NoiseModel, depolarizing_error\n\nnoise_model = NoiseModel()\nnoise_model.add_all_qubit_quantum_error(depolarizing_error(0.008, 1),\n                                        ['rx', 'ry', 'rz', 'id', 'sx', 'x'])\nnoise_model.add_all_qubit_quantum_error(depolarizing_error(0.02, 2),\n                                        ['cx', 'ecr', 'cz'])\nprint(\"Noise model constructed:\")\nprint(noise_model)\n\n# Conceptual ZNE demonstration (synthetic data)\nnoise_scales = np.array([1.0, 1.5, 2.0, 2.5, 3.0])\n# True noiseless value\ntrue_value = -1.137\n# Observed values degrade roughly linearly with scale (toy model)\nrng = np.random.default_rng(7)\nobserved = true_value + 0.045 * noise_scales + rng.normal(0, 0.004, size=noise_scales.shape)\n\n# Linear fit and extrapolation to scale = 0\ncoef = np.polyfit(noise_scales, observed, 1)\nextrapolated = np.polyval(coef, 0.0)\n\nfig, ax = plt.subplots(figsize=(8.5, 5))\nax.plot(noise_scales, observed, \"o\", markersize=10, color=\"#DD8452\",\n        label=\"Noisy estimates (different scale factors)\", zorder=5)\nx_line = np.linspace(0, 3.2, 50)\nax.plot(x_line, np.polyval(coef, x_line), \"--\", color=\"#4C72B0\", lw=2, label=\"Linear fit\")\nax.scatter([0], [extrapolated], s=160, c=\"#55A868\", marker=\"*\", zorder=6,\n           edgecolors=\"k\", label=f\"ZNE result = {extrapolated:.4f}\")\nax.axhline(true_value, color=\"gray\", ls=\":\", label=f\"True value = {true_value:.4f}\")\nax.axvline(0, color=\"k\", lw=0.8)\nax.set_xlabel(\"Noise amplification scale factor\")\nax.set_ylabel(\"Estimated energy (Ha)\")\nax.set_title(\"Zero-Noise Extrapolation (ZNE) – Conceptual Example\", fontweight=\"bold\")\nax.legend(loc=\"upper left\")\nax.set_xlim(-0.2, 3.3)\nplt.tight_layout()\nplt.show()\n\nprint(\"Lab exercise: replace the synthetic points with real noisy VQE runs at several scale factors.\")\n"
  },
  {
   "cell_type": "markdown",
   "id": "b7584e7d",
   "metadata": {
    "id": "b7584e7d"
   },
   "source": "### 4.3 Intellectual Property & Commercial Pathways (Discussion Module)\n\n**Key topics for the live lecture**\n\n1. **Protectable assets**\n   - Novel active-space heuristics\n   - Hybrid classical–quantum workflow architectures\n   - Domain-specific error mitigation for chemistry operators\n   - Multi-paradigm (gate + annealing) software interfaces\n\n2. **International strategy**\n   - Priority filing → PCT within 12 months → national phases (US, EP, CN, JP, KR …)\n   - Trade-secret protection for certain classical pre-/post-processing components\n\n3. **Open-source vs proprietary**\n   - Core libraries (Qiskit Nature, PennyLane, PySCF) are open\n   - Competitive edge often lies in curated data, optimized pipelines and chemistry-specific mitigation\n\n4. **Commercial verticals**\n   - Battery materials, catalysts, energy storage – high-value application domains for quantum chemistry software\n"
  },
  {
   "cell_type": "markdown",
   "id": "64d9d7c8",
   "metadata": {
    "id": "64d9d7c8"
   },
   "source": "---\n# Course Completion & Next Steps\n\n### What you have accomplished\n- Built and **visualized** molecular Hamiltonians and active spaces\n- Executed and **diagrammed** UCCSD-VQE and qEOM\n- Trained quantum kernels and a QNN with **training curves, heatmaps and circuit drawings**\n- Explored Trotterized dynamics and **ZNE extrapolation graphics**\n- Understood the hardware mapping path to IBM Condor, Origin Wukong and D-Wave\n- Reviewed intellectual-property considerations\n\n### Recommended further work\n1. Replace synthetic QML targets with real perovskite / battery descriptors\n2. Implement a full ZNE loop on the H₂ or LiH VQE observable\n3. Transpile a UCCSD circuit to a real IBM backend and compare depth / gate counts\n4. Formulate a classification task as QUBO for D-Wave Leap\n5. Explore adaptive ansatze for larger active spaces\n\n### Core References\n- Peruzzo et al., Nat. Commun. 5, 4213 (2014)\n- McClean et al., New J. Phys. 18, 023023 (2016)\n- Cao et al., Chem. Rev. 119, 10856 (2019)\n\n---\n\n**Instructor:** Joseph Volkan Ozcan  \n**QCCM-601 – Practical Quantum Chemical Simulation on Advanced Global Hardware**\n"
  }
 ],
 "metadata": {
  "colab": {
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  },
  "kernelspec": {
   "display_name": "Python 3",
   "name": "python3"
  },
  "language_info": {
   "name": "python"
  }
 },
 "nbformat": 4,
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}