{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Qubit Protected by Two-Cooper-Pair Tunneling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, we try to reproduce the result of the [\"Superconducting circuit protected by two-Cooper-pair tunneling\"](https://www-nature-com.stanford.idm.oclc.org/articles/s41534-019-0231-2) paper."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introdcution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Smith2020](https://doi-org.stanford.idm.oclc.org/10.1038/s41534-019-0231-2)\n",
    "designed a qubit that is protected by two Cooper-pair tunneling. We reproduced the main results of the paper such as\n",
    "energy spectrum, wavefunctions, and matrix elements by use of SQcircuit. The diagram of the circuit is"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"pics/twoCPB_pic1.png\" width=\"300\" align=\"left\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The circuit consists of four equal inductors with $E_L=2\\text{GHz}$, two equal Josephson Junction with $E_J=15\\text{GHz}$ and $E_{C_J}=2\\text{GHz}$, and one shunt capacitor of $E_{C}=0.04\\text{GHz}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Circuit Description"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Firstly, we import the SQcircuit and the relavant libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import SQcircuit as sq\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from matplotlib.colors import LinearSegmentedColormap"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define the single inductive loop of the circuit via `Loop` class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "loop1 = sq.Loop()"
   ]
  },
  {
   "cell_type": "markdown",
   "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,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define the circuit elements\n",
    "CJ = sq.Capacitor(2, 'GHz', Q=1e6)\n",
    "Cshunt = sq.Capacitor(0.04, 'GHz')\n",
    "L = sq.Inductor(2,'GHz', loops = [loop1])\n",
    "JJ = sq.Junction(15,'GHz', loops = [loop1])\n",
    "\n",
    "# define the circuit\n",
    "elements = {\n",
    "    (0, 1): [L],\n",
    "    (0, 2): [L],\n",
    "    (1, 3): [CJ, JJ],\n",
    "    (2, 4): [CJ, JJ],\n",
    "    (3, 5): [L],\n",
    "    (4 ,5): [L],\n",
    "    (0, 5): [Cshunt]\n",
    "}\n",
    "\n",
    "cr = sq.Circuit(elements)"
   ]
  },
  {
   "cell_type": "markdown",
   "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,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\hat{H} =~\\omega_1\\hat a^\\dagger_1\\hat a_1~+~\\omega_2\\hat a^\\dagger_2\\hat a_2~+~E_{C_{33}}(\\hat{n}_3-n_{g_{3}})^2~~-~E_{J_{1}}\\cos(\\hat{\\varphi}_1-\\hat{\\varphi}_2+\\hat{\\varphi}_3-0.5\\varphi_{\\text{ext}_{1}})~-~E_{J_{2}}\\cos(\\hat{\\varphi}_1+\\hat{\\varphi}_2+\\hat{\\varphi}_3+0.5\\varphi_{\\text{ext}_{1}})$"
      ],
      "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": [
       "$\\text{mode}~1:~~~~~~~~~~~\\text{harmonic}~~~~~~~~~~~\\hat{\\varphi}_1~=~\\varphi_{zp_{1}}(\\hat a_1+\\hat a^\\dagger_1)~~~~~~~~~~~\\omega_1/2\\pi~=~4.07921~~~~~~~~~~~\\varphi_{zp_{1}}~=~9.71e-01$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\text{mode}~2:~~~~~~~~~~~\\text{harmonic}~~~~~~~~~~~\\hat{\\varphi}_2~=~\\varphi_{zp_{2}}(\\hat a_2+\\hat a^\\dagger_2)~~~~~~~~~~~\\omega_2/2\\pi~=~4.0~~~~~~~~~~~\\varphi_{zp_{2}}~=~1.00e+00$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\text{mode}~3:~~~~~~~~~~~\\text{charge}~~~~~~~~~~~~~~~~n_{g_{3}}~=~0$"
      ],
      "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": [
       "$\\text{parameters}:~~~~~~~~~~~E_{C_{33}}~=~0.154~~~~~~~~~~~E_{J_{1}}~=~15.0~~~~~~~~~~~E_{J_{2}}~=~15.0~~~~~~~~~~~$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\text{loops}:~~~~~~~~~~~~~~~~~~~~\\varphi_{\\text{ext}_{1}}/2\\pi~=~0.0~~~~~~~~~~~$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cr.description()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above output shows that `cr` circuit has two harmonic modes with one charge mode."
   ]
  },
  {
   "cell_type": "markdown",
   "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,
   "metadata": {},
   "outputs": [],
   "source": [
    "cr.set_trunc_nums([17,17,9])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Circuit Spectrum"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To generate the spectrum of the circuit, firstly, we need to change and sweep the external flux of `loop1` by the `set_flux()` method. Then, we need to find the eigenfrequencies of the circuit that correspond to that external flux via `diag()` method. The following lines of code find the `spec` a 2D NumPy array so that each column of it contains the eigenfrequencies with respect to its external flux. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# number of eigenvalues we aim for\n",
    "n_eig=6\n",
    "\n",
    "# array that contains the spectrum\n",
    "phi = np.linspace(-0.1,0.6,50)\n",
    "\n",
    "# array that contains the spectrum\n",
    "spec = np.zeros((n_eig, len(phi)))\n",
    "\n",
    "for i in range(len(phi)):\n",
    "    # set the value of the flux external flux\n",
    "    loop1.set_flux(phi[i])\n",
    "    \n",
    "    # diagonlize the circuit\n",
    "    spec[:, i], _ = cr.diag(n_eig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "E_L = 2\n",
    "E_C = 2\n",
    "x=0.02\n",
    "plt.figure()\n",
    "for i in range(n_eig):\n",
    "    plt.plot(phi, (spec[i, :] - spec[0, :])/np.sqrt(16*x*(E_L/2)*E_C))\n",
    "\n",
    "plt.xlabel(\"$\\Phi_{ext}/\\Phi_0$\", fontsize=13)\n",
    "plt.ylabel(r\"$f_i-f_0$[GHz]\", fontsize=13)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next cell shows the spectrum from the figure 3a of the paper, which is the same spectrum that SQcircuit calculated."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"pics/twoCPB_pic2.png\" width=\"400\" align = \"left\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Eigenfunctions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can get the phase space eigenfunction of a specific eigenvector of a circuit by using the `eig_phase_coord()` method. To calculate the eigenfunction at $\\Phi_{ext} = 0.5\\Phi_0$ similar to paper, we set back the flux of our loop to $0.5$ and diagonalize the `cr` again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "loop1.set_flux(0.5)\n",
    "cr.set_trunc_nums([17,17,17])\n",
    "_, _ = cr.diag(n_eig=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We generate the eigenfunction in the phase space by `eig_phase_coord()` method for the first four eigen state of the circuit similar to the paper."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create a range for each mode\n",
    "phi1 = 0\n",
    "phi2 = np.linspace(-0.8,0.8,100)\n",
    "phi3 = np.pi*np.linspace(-1.5,2.5,100)\n",
    "\n",
    "# creat the grid list\n",
    "grid = [phi1, phi2, phi3]\n",
    "\n",
    "# the ground state\n",
    "state0 = cr.eig_phase_coord(0, grid = grid)\n",
    "    \n",
    "# the first excited state\n",
    "state1 = cr.eig_phase_coord(1, grid = grid)\n",
    "\n",
    "# the second excited state\n",
    "state2 = cr.eig_phase_coord(2, grid = grid)\n",
    "    \n",
    "# the third excited state\n",
    "state3 = cr.eig_phase_coord(3, grid = grid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 4,figsize=(16,4), sharey='row')\n",
    "axs[0].pcolor(phi3, phi2, np.abs(state0.T)**2,cmap=\"Purples\",shading='auto',label='state0')\n",
    "axs[1].pcolor(phi3, phi2, np.abs(state1.T)**2,cmap=\"Greens\",shading='auto',label='state1')\n",
    "axs[2].pcolor(phi3, phi2, np.abs(state2.T)**2,cmap=\"Oranges\",shading='auto',label='state2')\n",
    "axs[3].pcolor(phi3, phi2, np.abs(state3.T)**2,cmap=\"Reds\",shading='auto',label='state3')\n",
    "for i in range(4):\n",
    "    axs[i].set_xlabel(r\"$\\varphi_2$\",fontsize=13)\n",
    "    axs[i].legend(handletextpad=-0.1, handlelength=0.0)\n",
    "axs[0].set_ylabel(r\"$\\varphi_3$\",fontsize=13)\n",
    "plt.subplots_adjust(wspace=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next cell shows the eigenfunctions from the figure 3c of the paper, which is the same as what SQcircuit calculated."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"pics/twoCPB_pic3.png\" width=\"800\" align = \"left\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matrix Elements"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Smith2020](https://doi-org.stanford.idm.oclc.org/10.1038/s41534-019-0231-2) defined the normalized matrix element as a measure of degree of freedoms to which circuit can couple. For coupling operator $\\mathcal{O}$ the normalized matrix element is"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"pics/twoCPB_pic4.png\" width=\"220\" align = \"left\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where $|\\psi\\rangle$ is the eigenstates of the circuit and $|0o\\rangle$ is the ground state. We calculate the normalized matrix element for inductive coupling to inductor between node 0 and node 2 using `cr.coupling_op()` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "n_eig = 2\n",
    "phi = np.linspace(0.46, 0.54, 1000)\n",
    "# normalized matrix element\n",
    "inductive_01 = np.zeros(len(phi))\n",
    "\n",
    "for i in range(len(phi)):\n",
    "#     print(i)\n",
    "    loop1.set_flux(phi[i])\n",
    "    evals, estates = cr.diag(n_eig)\n",
    "    O = cr.coupling_op(\"inductive\", nodes=(2,0))\n",
    "    norm = (estates[0].dag()*(O.dag()*O)*estates[0])[0].real\n",
    "    inductive_01[i] =  np.abs((estates[0].dag()*O*estates[1])[0])**2/norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f804320e9a0>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(phi, inductive_01, 'green')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next figure shows the same result from the figure 4a of the paper."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"pics/twoCPB_pic5.png\" width=\"300\" 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": 2
}