{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ff54523e",
   "metadata": {},
   "source": [
    "# Kite Circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9faf5f96",
   "metadata": {},
   "source": [
    "In this notebook, we try to reproduce the result of the [\"Magnifying Quantum Phase Fluctuations with Cooper-Pair Pairing\"](https://journals.aps.org/prx/abstract/10.1103/PhysRevX.12.021002) paper."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79f4f387",
   "metadata": {},
   "source": [
    "## Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0117e38",
   "metadata": {},
   "source": [
    "[Smith2022](https://journals.aps.org/prx/abstract/10.1103/PhysRevX.12.021002) designed a superconducting circuit that maginfies quantum phase fluctuations with Cooper-pair pairing. We reproduced the energy spectrum of the Kite circuit. The diagram of the circuit is"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a16a877",
   "metadata": {},
   "source": [
    "<img src=\"pics/kite_pic1.png\" width=\"300\" align=\"left\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9b9c440",
   "metadata": {},
   "source": [
    "The parameters for these device in gigahertz unit are as following"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c098e65",
   "metadata": {},
   "source": [
    "<img src=\"pics/kite_pic2.png\" width=\"450\" align=\"left\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd27f1f5",
   "metadata": {},
   "source": [
    "## Circuit Description"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "895d6479",
   "metadata": {},
   "source": [
    "Firstly, we import the SQcircuit and the relavant libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "bce699a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import SQcircuit as sq\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "451569cc",
   "metadata": {},
   "source": [
    "We define the two inductive loops of the circuit via `Loop` class. `loop1` represents $\\theta_\\text{ext}$ and `loop2` represents $\\varphi_\\text{ext}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f2f2dabe",
   "metadata": {},
   "outputs": [],
   "source": [
    "# theta_ext:\n",
    "loop1 = sq.Loop()\n",
    "# phi_ext:\n",
    "loop2 = sq.Loop()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e7dcad4",
   "metadata": {},
   "source": [
    "The elements of the circuit can be defined via `Capacitor`, `Inductor`, and `Junction` classes in SQcircuit, and to define the circuit, we use the `Circuit` class. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5cb243f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "C = sq.Capacitor(2.5)\n",
    "CJ = sq.Capacitor(6.6)\n",
    "JJ1 = sq.Junction(5.9, loops =[loop1])\n",
    "JJ2 = sq.Junction(5.9, loops =[loop1, loop2])\n",
    "l1 = sq.Inductor(0.36, loops =[loop1])\n",
    "l2 = sq.Inductor(0.36, loops =[loop1, loop2])\n",
    "L = sq.Inductor(0.23, loops=[loop2])\n",
    "\n",
    "elements = {\n",
    "    (0, 1): [l1],\n",
    "    (0, 2): [l2],\n",
    "    (0, 3): [L, C],\n",
    "    (1, 3): [JJ1, CJ],\n",
    "    (2, 3): [JJ2, CJ]\n",
    "}\n",
    "\n",
    "kite = sq.Circuit(elements)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b864cd36",
   "metadata": {},
   "source": [
    "By creating an object of `Circuit` class, SQcircuit systematically finds the correct set of transformations and basis to make the circuit ready to be diagonalized.\n",
    "\n",
    "Before setting the truncation numbers for each mode and diagonalizing the Hamiltonian, we can gain more insight into our circuit by calling the `description()` method. This prints out the Hamiltonian and a listing of the modes, whether they are harmonic or charge modes, and the frequency for each harmonic in GHz (the default unit). Moreover, it shows the prefactors in the Josephson junction part of the Hamiltonian $\\tilde{\\textbf{w}}_k$, which helps find the modes decoupled from the nonlinearity of the circuit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7493e1b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\hat{H} =~\\omega_1\\hat a^\\dagger_1\\hat a_1~+~\\omega_2\\hat a^\\dagger_2\\hat a_2~+~\\omega_3\\hat a^\\dagger_3\\hat a_3~~-~E_{J_{1}}\\cos(-\\hat{\\varphi}_1+\\hat{\\varphi}_2-\\hat{\\varphi}_3-\\varphi_{\\text{ext}_{1}}-\\varphi_{\\text{ext}_{2}})~-~E_{J_{2}}\\cos(-\\hat{\\varphi}_1-\\hat{\\varphi}_2-\\hat{\\varphi}_3-\\varphi_{\\text{ext}_{2}})$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$------------------------------------------------------------$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\text{mode}~1:~~~~~~~~~~~\\text{harmonic}~~~~~~~~~~~\\hat{\\varphi}_1~=~\\varphi_{zp_{1}}(\\hat a_1+\\hat a^\\dagger_1)~~~~~~~~~~~\\omega_1/2\\pi~=~5.96222~~~~~~~~~~~\\varphi_{zp_{1}}~=~1.05e+00$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\text{mode}~2:~~~~~~~~~~~\\text{harmonic}~~~~~~~~~~~\\hat{\\varphi}_2~=~\\varphi_{zp_{2}}(\\hat a_2+\\hat a^\\dagger_2)~~~~~~~~~~~\\omega_2/2\\pi~=~4.3598~~~~~~~~~~~\\varphi_{zp_{2}}~=~1.74e+00$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\text{mode}~3:~~~~~~~~~~~\\text{harmonic}~~~~~~~~~~~\\hat{\\varphi}_3~=~\\varphi_{zp_{3}}(\\hat a_3+\\hat a^\\dagger_3)~~~~~~~~~~~\\omega_3/2\\pi~=~1.56833~~~~~~~~~~~\\varphi_{zp_{3}}~=~2.05e+00$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$------------------------------------------------------------$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\text{parameters}:~~~~~~~~~~~E_{J_{1}}~=~5.9~~~~~~~~~~~E_{J_{2}}~=~5.9~~~~~~~~~~~$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\text{loops}:~~~~~~~~~~~~~~~~~~~~\\varphi_{\\text{ext}_{1}}/2\\pi~=~0.0~~~~~~~~~~~\\varphi_{\\text{ext}_{2}}/2\\pi~=~0.0~~~~~~~~~~~$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kite.description()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "940b972c",
   "metadata": {},
   "source": [
    "To determine the size of the Hilbert space, we specify the truncation number for each circuit mode via `set_trunc_nums()` method. Note that this is a necessary step before diagonalizing the circuit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "969f0c43",
   "metadata": {},
   "outputs": [],
   "source": [
    "kite.set_trunc_nums([15,15,15])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a776cdf3",
   "metadata": {},
   "source": [
    "## Circuit Spectrum"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02ae29ba",
   "metadata": {},
   "source": [
    "We calculate the spectrum of the circuit for $\\theta_\\text{ext}=0$ and sweep $\\phi_\\text{ext}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c4c4494f",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "n_eig = 7\n",
    "phi_ext = np.linspace(-0.25, 1.25, 30)\n",
    "\n",
    "spec = np.zeros((n_eig, len(phi_ext)))\n",
    "\n",
    "for i, phi in enumerate(phi_ext):\n",
    "#     print(i)\n",
    "    loop1.set_flux(0)\n",
    "    loop2.set_flux(phi)\n",
    "    spec[:, i], _ = kite.diag(n_eig=n_eig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1615d0ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(4, 6))\n",
    "for i in range(n_eig):\n",
    "    plt.plot(phi_ext, (spec[i, :] - spec[0, :]), '.-')\n",
    "\n",
    "plt.title(r\"$\\theta_{ext} = 0$\", fontsize=13)\n",
    "plt.xlabel(r\"$\\Phi_{ext}/\\Phi_0$\", fontsize=13)\n",
    "plt.ylabel(r\"($\\omega_i-\\omega_0$)GHz\", fontsize=13)\n",
    "plt.xticks([0, 0.5, 1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee3f9e50",
   "metadata": {},
   "source": [
    "We calculate the spectrum of the circuit for $\\theta_\\text{ext}=\\pi$ and sweep $\\phi_\\text{ext}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "31387795",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "n_eig = 7\n",
    "phi_ext = np.linspace(-0.25, 1.25, 30)\n",
    "\n",
    "spec = np.zeros((n_eig, len(phi_ext)))\n",
    "\n",
    "for i, phi in enumerate(phi_ext):\n",
    "#     print(i)\n",
    "    loop1.set_flux(0.5)\n",
    "    loop2.set_flux(phi)\n",
    "    spec[:, i], _ = kite.diag(n_eig=n_eig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "3e41ccda",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(4, 6))\n",
    "for i in range(n_eig):\n",
    "    plt.plot(phi_ext, (spec[i, :] - spec[0, :]), '.-')\n",
    "\n",
    "plt.title(r\"$\\theta_{ext} = \\pi$\", fontsize=13)\n",
    "plt.xlabel(r\"$\\Phi_{ext}/\\Phi_0$\", fontsize=13)\n",
    "plt.ylabel(r\"($\\omega_i-\\omega_0$)GHz\", fontsize=13)\n",
    "plt.xticks([0, 0.5, 1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85245eda",
   "metadata": {},
   "source": [
    "The next cell shows the spectrum from the figure 5 of the paper, which is the same spectrum that SQcircuit calculated for $\\theta_\\text{ext}=0$ and $\\theta_\\text{ext}=\\pi$. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f52ad216",
   "metadata": {},
   "source": [
    "<img src=\"pics/kite_pic3.png\" width=\"750\" align=\"left\"/>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}