{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "075bd937-5d0c-4e29-8351-faa413a5f7d1",
   "metadata": {},
   "source": [
    "# 4.19 Analyse a Transmon Qubit using ElmerFEM\n",
    "This notebook demonstrates the new open-source rendering and simulation capabilities of Qiskit Metal using `Gmsh` and `ElmerFEM` for tuning the performance parameters of a transmon qubit. instructions to download and install this branch of Qiskit Metal with Gmsh and ElmerFEM, can he found [here](https://github.com/Qiskit/qiskit-metal/blob/elmer_renderer/tutorials/4%20Analysis/B.%20Advanced%20-%20Direct%20use%20of%20the%20renderers/Gmsh-Elmer-install-instructions.md) The tutorial has the following steps:\n",
    "\n",
    "## Contents\n",
    "### 1. Creating a Transmon Qubit in Qiskit Metal\n",
    "### 2. Rendering and meshing your design in the `QGmshRenderer`\n",
    "- Rendering the design wireframe\n",
    "- Applying a basic mesh\n",
    "- Customizing the mesh\n",
    "    - Setting initial mesh size parameters\n",
    "    - Using the Intelli-mesh feature in `QGmshRenderer`\n",
    "- Saving your mesh to a file\n",
    "\n",
    "### 3. Rendering your design in `QElmerRenderer` (uses `QGmshRenderer`)\n",
    "- Render design and generate mesh\n",
    "- Export the mesh\n",
    "- Run the capacitance simulation\n",
    "    - Add solution setup\n",
    "    - Run the solver\n",
    "    - Export capacitance matrix\n",
    "\n",
    "### 4. Perform LOM 2.0 Analysis\n",
    "- Import the capacitance matrix\n",
    "- Define cells and subsystems\n",
    "- Define the composite system\n",
    "- Compute the results:\n",
    "    - Qubit Frequency ($f_Q$)\n",
    "    - Anharmonicity ($\\alpha$)\n",
    "    - Readout $\\chi$\n",
    "    - Coupling $g$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cfbf8541",
   "metadata": {},
   "source": [
    "> 💡 **Using this tutorial without the Qt GUI**\n",
    "> \n",
    "> This tutorial uses the desktop `MetalGUI`. To follow along on Colab, Binder, JupyterHub, or any environment where Qt isn't available, **replace any `gui.rebuild()` / `gui.screenshot()` call with `qm.view(design)`** — it renders the design to a matplotlib `Figure` you can display inline or save with `fig.savefig(...)`.\n",
    "> \n",
    "> See [1.4 Headless quick view](../1-Overview/1.4-Headless-quick-view-%28no-Qt-GUI%29.ipynb) for a complete runnable walkthrough and [`docs/headless-usage.rst`](../../../docs/headless-usage.rst) for the full reference."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be3cbb43-2c24-4139-b690-1d56047a03c5",
   "metadata": {},
   "source": [
    "## Necessary Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "28f8c32e-5341-49d6-b63f-0e16419b162c",
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "# Import basic things of Qiskit Metal\n",
    "from qiskit_metal import MetalGUI, designs\n",
    "from qiskit_metal.qlibrary.qubits.transmon_pocket_6 import TransmonPocket6\n",
    "\n",
    "# Import the Gmsh renderer\n",
    "from qiskit_metal.renderers.renderer_gmsh.gmsh_renderer import QGmshRenderer\n",
    "\n",
    "# Import the Elmer renderer\n",
    "from qiskit_metal.renderers.renderer_elmer.elmer_renderer import QElmerRenderer\n",
    "from qiskit_metal.renderers.renderer_elmer.elmer_renderer import (\n",
    "    load_capacitance_matrix_from_file,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a76242c0-3b42-4157-bbcb-a99b3c47937a",
   "metadata": {},
   "outputs": [],
   "source": [
    "%metal_heading 1. Create a Transmon Qubit in Qiskit Metal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "31a7b793-64a5-44c6-9176-718f9b7c1c66",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Instantiate a design object\n",
    "design = designs.MultiPlanar({}, True)\n",
    "\n",
    "# Invoke the Qiskit Metal GUI\n",
    "gui = MetalGUI(design)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6fe517d6-d32f-417c-a8fa-33061c2e54c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define a dictionary for connection pad options for the transmon\n",
    "conn_pads = dict(\n",
    "    connection_pads=dict(\n",
    "        readout=dict(loc_W=0, loc_H=-1),\n",
    "        coupler1=dict(loc_W=-1, loc_H=1),\n",
    "        coupler2=dict(loc_W=1, loc_H=1),\n",
    "    )\n",
    ")\n",
    "\n",
    "# Create a TransmonPocket6 object\n",
    "q1 = TransmonPocket6(design, \"Q1\", options=dict(**conn_pads))\n",
    "\n",
    "# Rebuild and autoscale the GUI\n",
    "gui.rebuild()\n",
    "gui.autoscale()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d97e061c-fbcc-4419-a30c-8854b8c63444",
   "metadata": {},
   "outputs": [],
   "source": [
    "%metal_heading 2. Rendering and meshing your design in the `QGmshRenderer`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f118489-71a8-494f-8c1b-b6cc837382c3",
   "metadata": {},
   "source": [
    "## Rendering the design wireframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "713202e1-dedc-469d-8dc3-9fe99496e42e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Instantiate the Gmsh renderer\n",
    "gmsh_renderer = QGmshRenderer(design)\n",
    "\n",
    "# Render the design\n",
    "# Tip: `mesh_geoms = False` will not mesh the design,\n",
    "# but only draw the wire-frame of the geomtries\n",
    "gmsh_renderer.render_design(\n",
    "    open_pins=[(\"Q1\", \"coupler1\"), (\"Q1\", \"coupler2\"), (\"Q1\", \"readout\")],\n",
    "    mesh_geoms=False,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "eef5a352-24f3-4257-968f-be197eeba30d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Launch Gmsh GUI to see the rendererd design\n",
    "gmsh_renderer.launch_gui()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cea57dd6-816f-4649-a77c-e9b774dcc153",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Applying a basic mesh"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "545d393c-8d57-4914-9dbc-92e8a0f32b0e",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Add a basic mesh to the design and luanch the GUI to view\n",
    "gmsh_renderer.add_mesh(dim=3, intelli_mesh=False)\n",
    "gmsh_renderer.launch_gui()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6347235c-d319-4c61-a981-7e4005b25d15",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Customizing the mesh\n",
    "### Setting initial mesh size parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b851f19f-e8d0-479e-b0ae-056fa8a47e9f",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Update the mesh options\n",
    "gmsh_renderer.options.mesh.min_size = \"5um\"\n",
    "gmsh_renderer.options.mesh.max_size = \"20um\"\n",
    "\n",
    "# Render the design\n",
    "gmsh_renderer.render_design(\n",
    "    open_pins=[(\"Q1\", \"coupler1\"), (\"Q1\", \"coupler2\"), (\"Q1\", \"readout\")],\n",
    "    mesh_geoms=False,\n",
    ")\n",
    "\n",
    "# Mesh the design (without intelli-mesh)\n",
    "gmsh_renderer.add_mesh(intelli_mesh=False)\n",
    "gmsh_renderer.launch_gui()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44bc0221-43d2-4551-b69d-4ab4f3f5b416",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Using the Intelli-mesh feature in QGmshRenderer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4b02fbf9-2717-45b8-9293-3bd1121862f9",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Update the mesh options\n",
    "gmsh_renderer.options.mesh.min_size = \"5um\"\n",
    "gmsh_renderer.options.mesh.max_size = \"50um\"\n",
    "\n",
    "# Render and mesh the design (with intelli-mesh)\n",
    "gmsh_renderer.render_design(\n",
    "    open_pins=[(\"Q1\", \"coupler1\"), (\"Q1\", \"coupler2\"), (\"Q1\", \"readout\")],\n",
    "    mesh_geoms=True,\n",
    ")\n",
    "gmsh_renderer.launch_gui()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f441adcc-510f-4c8a-8516-1caf7dcb9166",
   "metadata": {},
   "source": [
    "## Saving your mesh to a file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "af6556de-1546-47b5-8f26-9227af19ff86",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Export the Gmsh generated mesh to a file\n",
    "gmsh_renderer.export_mesh(\"test.msh\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3672846f-b035-4eab-80a9-3c199eb4fd7c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Close the Gmsh renderer\n",
    "gmsh_renderer.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "88883f88-342e-449c-a1ce-c253a28c0145",
   "metadata": {},
   "outputs": [],
   "source": [
    "%metal_heading 3. Rendering your design in `QElmerRenderer` (uses `QGmshRenderer`)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8c2f7a6a-f6ed-4892-96c3-a62f866ef37c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Instantiate the Elmer renderer\n",
    "elmer_renderer = QElmerRenderer(design)\n",
    "\n",
    "# Elmer renderer uses the Gmsh renderer to\n",
    "# generate a mesh for the design\n",
    "# Set initial parameters for meshing in Gmsh (IMPORTANT step!!)\n",
    "elmer_renderer.gmsh.options.mesh.min_size = \"5um\"\n",
    "elmer_renderer.gmsh.options.mesh.max_size = \"50um\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e7c297c2-be7e-495b-b98a-4062cab91be0",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Render the design\n",
    "elmer_renderer.render_design(\n",
    "    open_pins=[(\"Q1\", \"coupler1\"), (\"Q1\", \"coupler2\"), (\"Q1\", \"readout\")],\n",
    "    skip_junctions=True,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "43145408-a90f-4e75-921d-ca8eafd5ea7e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# View the generated mesh\n",
    "elmer_renderer.launch_gmsh_gui()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ab7e7c7a-9207-4943-bf0f-1d183a8d007c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Export the generated mesh\n",
    "elmer_renderer.export_mesh()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5cc8b22f-f281-45c3-a53a-f2a7c9a29fed",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Add a solution setup to solve for the capacitance matrix\n",
    "elmer_renderer.add_solution_setup(\"capacitance\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "020dc57e-d668-4d7b-b8fc-62fcceb6468d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Run the simulation in ElmerFEM\n",
    "elmer_renderer.run(\"capacitance\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b250b918-1cd7-429d-b015-92b114bf2594",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Display the capacitnce matrix obtained after the simulation\n",
    "elmer_renderer.capacitance_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "07625769-38c4-4be7-9c64-9e4e7b993506",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Run this, and in the Gmsh window,\n",
    "# Right click on an empty area, click on \"Toggle mesh visibility\"\n",
    "# Next, go to: Tools -> Visibility, select \"Physical groups\" in drop down menu\n",
    "# Select \"Volume 2\", click on apply\n",
    "# On the left pane, click on \"Post-processing\", and select the views that you want to observe\n",
    "elmer_renderer.display_post_processing_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ca5cf807-4323-48d8-b6cd-f5e38f3b24d3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Export the capacitance matrix\n",
    "elmer_renderer.save_capacitance_matrix(\"cap_matrix.txt\")\n",
    "\n",
    "# Close the elmer renderer\n",
    "elmer_renderer.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b20674ae-918f-4aa7-b4f7-1a337ae714a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "%metal_heading 4. Perform LOM 2.0 Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "603f8d95-ac34-40e0-9574-53d0f6cde2b8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import necessary things for LOM 2.0 Analysis\n",
    "import numpy as np\n",
    "from qiskit_metal.analyses.quantization.lom_core_analysis import (\n",
    "    CompositeSystem,\n",
    "    Cell,\n",
    "    Subsystem,\n",
    ")\n",
    "from scipy.constants import speed_of_light as c_light\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cf3df357-f1fe-4bd0-9510-02fd7e2a55bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load the saved capacitance matrix\n",
    "cap_matrix = load_capacitance_matrix_from_file(\"cap_matrix.txt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9705e531-ef68-4b6b-bbc6-6a8b69ba0a12",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define cells\n",
    "opt1 = dict(\n",
    "    node_rename={\n",
    "        \"Q1_coupler1_connector_pad\": \"coupler1\",\n",
    "        \"Q1_coupler2_connector_pad\": \"coupler2\",\n",
    "        \"Q1_readout_connector_pad\": \"readout\",\n",
    "    },\n",
    "    cap_mat=cap_matrix,\n",
    "    ind_dict={(\"Q1_pad_top\", \"Q1_pad_bot\"): 12},  # junction inductance in nH\n",
    "    jj_dict={(\"Q1_pad_top\", \"Q1_pad_bot\"): \"j1\"},\n",
    "    cj_dict={(\"Q1_pad_top\", \"Q1_pad_bot\"): 2},  # junction capacitance in fF\n",
    ")\n",
    "cell_1 = Cell(opt1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d5c8c296-13f9-4ec9-8daf-96f2f882b923",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define subsystems\n",
    "# subsystem 1: Transmon\n",
    "transmon = Subsystem(name=\"transmon1_sys\", sys_type=\"TRANSMON\", nodes=[\"j1\"])\n",
    "\n",
    "# subsystem 2: Coupler 1\n",
    "q_opts = dict(\n",
    "    f_res=7.4,  # resonator dressed frequency in GHz\n",
    "    Z0=50,  # characteristic impedance in Ohm\n",
    "    vp=0.404314 * c_light,  # phase velocity\n",
    ")\n",
    "coup1 = Subsystem(\n",
    "    name=\"coup1_sys\", sys_type=\"TL_RESONATOR\", nodes=[\"coupler1\"], q_opts=q_opts\n",
    ")\n",
    "\n",
    "# subsystem 3: Coupler 2\n",
    "q_opts = dict(\n",
    "    f_res=7.2,  # resonator dressed frequency in GHz\n",
    "    Z0=50,  # characteristic impedance in Ohm\n",
    "    vp=0.404314 * c_light,  # phase velocity\n",
    ")\n",
    "coup2 = Subsystem(\n",
    "    name=\"coup2_sys\", sys_type=\"TL_RESONATOR\", nodes=[\"coupler2\"], q_opts=q_opts\n",
    ")\n",
    "\n",
    "# subsystem 4: Readout\n",
    "q_opts = dict(\n",
    "    f_res=7,  # resonator dressed frequency in GHz\n",
    "    Z0=50,  # characteristic impedance in Ohm\n",
    "    vp=0.404314 * c_light,  # phase velocity\n",
    ")\n",
    "readout = Subsystem(\n",
    "    name=\"readout_sys\", sys_type=\"TL_RESONATOR\", nodes=[\"readout\"], q_opts=q_opts\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4f44c894-aa2b-4632-b513-da391f101b93",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the composite system\n",
    "composite_sys = CompositeSystem(\n",
    "    subsystems=[transmon, coup1, coup2, readout],\n",
    "    cells=[cell_1],\n",
    "    grd_node=\"ground_plane\",\n",
    "    nodes_force_keep=[\"coupler1\", \"coupler2\", \"readout\"],\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "86f39d01-c88f-4300-987f-0384703daf61",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get the circuit graph object\n",
    "cg = composite_sys.circuitGraph()\n",
    "print(cg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "19fee4da-5659-4b3b-ad29-182565ee8933",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a hilbert space with the composite system\n",
    "hilbertspace = composite_sys.create_hilbertspace()\n",
    "print(hilbertspace)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c18d596f-1778-4bf1-852c-6a3c7c8dc927",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Add interaction between the subsystems\n",
    "hilbertspace = composite_sys.add_interaction()\n",
    "\n",
    "# Get the total hamiltonian of the composite system\n",
    "hilbertspace.hamiltonian()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b4c2cdfb-6ede-46eb-bbaf-c19f75b9a5d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get the reults from the hamiltonian\n",
    "# Qubit frequency\n",
    "# Chi matrix (having anharmonicity and readout chi values)\n",
    "hamiltonian_results = composite_sys.hamiltonian_results(hilbertspace, evals_count=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8c01e33b-c8fa-464a-bd02-fa8e87f48b5a",
   "metadata": {},
   "outputs": [],
   "source": [
    "chi_df = hamiltonian_results[\"chi_in_MHz\"].to_dataframe()\n",
    "print(\n",
    "    \"Transmon frequency     :\", hamiltonian_results[\"fQ_in_Ghz\"][\"transmon1_sys\"], \"GHz\"\n",
    ")\n",
    "print(\"Transmon Anharmonicity :\", chi_df[\"transmon1_sys\"][\"transmon1_sys\"], \"MHz\")\n",
    "print(\"Readou chi             :\", chi_df[\"readout_sys\"][\"transmon1_sys\"], \"MHz\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "afdfe557-8d48-4a18-85bf-923aa2b63c07",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get the coupling 'g' values between qubit and resonators\n",
    "composite_sys.compute_gs().to_dataframe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "963212c4-b31f-48c0-ac56-0058e477b9e0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Hamiltonian parameters for the transmon\n",
    "transmon.h_params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "44627014-50d7-4f5c-b873-c7c438d6c6da",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Close the Qiskit Metal GUI\n",
    "gui.main_window.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9c3428fa-7009-451d-9032-a54ecf888791",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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