{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-27T13:40:22.157500Z",
     "start_time": "2019-08-27T13:40:18.878500Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from qucat import GUI\n",
    "from scipy.constants import pi,hbar, h, e"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Understanding a tuneable coupler circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we study the circuit of https://arxiv.org/abs/1802.10037 where two transmon qubits are coupled through a tuneable coupler.\n",
    "\n",
    "This tuneable coupler is built from a capacitor and a Superconducting Quantum Interference Device, or SQUID.\n",
    "By flux biasing the SQUID, we change the effective Josephson energy of the coupler, which modifies the coupling between the two transmons.\n",
    "We will present how the normal mode visualization tool helps in understanding the physics of the device.\n",
    "Secondly, we will show how a Hamiltonian generated with QuCAT accurately reproduces experimental measurements of the device.\n",
    "\n",
    "We start by building the device shown below\n",
    "\n",
    "![](graphics/TC_circuit.png)\n",
    "\n",
    "*optical micrograph from https://arxiv.org/abs/1802.10037*\n",
    "\n",
    "More specifically, we are interested in the part of the device in the dashed box, consisting of the two transmons and the tuneable coupler.\n",
    "The other circuitry, the flux line, drive line and readout resonator could be included to determine external losses, or the dispersive coupling of the transmons to their readout resonator.\n",
    "We will omit these features for simplicity here.\n",
    "\n",
    "The circuit is built with the GUI"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-27T13:40:49.515000Z",
     "start_time": "2019-08-27T13:40:22.162500Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 528x248.4 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "TC = GUI('circuits/tuneable_coupler.txt', # location of the circuit file\n",
    "        edit=True, # open the GUI to edit the circuit\n",
    "        plot=True, # plot the circuit after having edited it\n",
    "        print_network=False) # print the network"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The inductance $L_j$ of the junction which models the SQUID is given symbolically, and will have to be specified when calling future functions.\n",
    "Since $L_j$ is controlled through flux $\\phi$ in the experiment, we define a function which translates $\\phi$ (in units of the flux quantum) to $L_j$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-27T13:40:49.541000Z",
     "start_time": "2019-08-27T13:40:49.522000Z"
    }
   },
   "outputs": [],
   "source": [
    "def Lj(phi):\n",
    "    # maximum Josephson energy\n",
    "    Ejmax = 6.5e9\n",
    "    # junction asymmetry\n",
    "    d = 0.0769\n",
    "    # flux to Josephson energy\n",
    "    Ej = Ejmax*np.cos(pi*phi) *np.sqrt(1+d**2 *np.tan(pi*phi)**2)\n",
    "    # Josephson energy to inductance\n",
    "    return (hbar/2/e)**2/(Ej*h)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get an initial idea of the different modes of the circuit, let us display their resonance frequencies, their dissipation rates, anharmonicities and Kerr coefficients at 0 flux"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-27T13:42:08.220700Z",
     "start_time": "2019-08-27T13:42:08.179700Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         mode |       freq.  |       diss.  |       anha.  |\n",
      "            0 |     3.27 GHz |          0Hz |      165 MHz |\n",
      "            1 |     6.84 GHz |          0Hz |      128 MHz |\n",
      "            2 |     6.98 GHz |          0Hz |      117 MHz |\n",
      "\n",
      "Kerr coefficients (diagonal = Kerr, off-diagonal = cross-Kerr)\n",
      "         mode |         0    |         1    |         2    |\n",
      "            0 |      165 MHz |              |              |\n",
      "            1 |       13 MHz |      128 MHz |              |\n",
      "            2 |     94.8 MHz |      234 MHz |      117 MHz |\n",
      "\n"
     ]
    }
   ],
   "source": [
    "f,k,A,chi = TC.f_k_A_chi(pretty_print=True, Lj=Lj(0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-23T15:56:11.644300Z",
     "start_time": "2019-08-23T15:56:11.603300Z"
    }
   },
   "source": [
    "By visualizing the normal modes of the circuit, we can understand the mechanism behind the tuneable coupler.\n",
    "We plot the highest frequency mode at $\\phi=0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-23T16:20:43.169900Z",
     "start_time": "2019-08-23T16:20:42.628900Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Anaconda3\\lib\\site-packages\\qucat\\core.py:2499: RuntimeWarning: invalid value encountered in sqrt\n",
      "  return np.sqrt(hbar/np.real(z)/np.imag(dY(z,**kwargs)))\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 792x411.84 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "TC.show_normal_mode(mode = 2, \n",
    "    quantity = 'current',\n",
    "    Lj=Lj(0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This mode is called symmetric since the currents flow in the same direction on each side of the coupler.\n",
    "This leads to a net current through the coupler junction, such that the value of $L_j$ influences the oscillation frequency of the mode.\n",
    "Conversely, if we plot the anti-symmetric mode instead"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-23T16:20:43.611900Z",
     "start_time": "2019-08-23T16:20:43.170900Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 792x411.84 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "TC.show_normal_mode(mode = 1, \n",
    "    quantity = 'current',\n",
    "    Lj=Lj(0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "currents are flowing away from the coupler in each transmon, we find a current through the coupler junction and capacitor on the order of $10^{-21}$ A.\n",
    "This mode frequency should not vary as a function of $L_j$.\n",
    "When the bare frequency of the coupler matches the coupled transmon frequencies, the coupler acts as a band-stop filter, and lets no current traverse.\n",
    "At this point, both symmetric and anti-symmetric modes should have identical frequencies.\n",
    "\n",
    "This effect is shown experimentally in Fig. 2(e) of https://arxiv.org/abs/1802.10037.\n",
    "\n",
    "We can reproduce this experiment by generating a Hamiltonian with QuCAT and diagonalizing it with QuTiP for different values of the flux."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-23T16:20:51.948900Z",
     "start_time": "2019-08-23T16:20:43.613900Z"
    }
   },
   "outputs": [],
   "source": [
    "# modes to include when generating the system Hamiltonian\n",
    "modes_to_include = [1,2]\n",
    "\n",
    "# Values of the bias flux to sweep\n",
    "phi_list = np.linspace(-0.25,0.5,201)\n",
    "\n",
    "# Iitialize a list of transition frequencies\n",
    "fs = [np.zeros(len(phi_list)) for mode in modes_to_include]\n",
    "\n",
    "for i,phi in enumerate(phi_list):\n",
    "    # Generate the Hamiltonian\n",
    "    H = TC.hamiltonian(\n",
    "        Lj = Lj(phi), \n",
    "        excitations = 7, \n",
    "        taylor = 4, \n",
    "        modes = modes_to_include)\n",
    "    \n",
    "    # compute eigenenergies and eigenstates\n",
    "    ee,es = H.eigenstates()\n",
    "    \n",
    "    # Add the first two transition frequencies of the \n",
    "    # two modes considered to the list of transition frequencies\n",
    "    for m,mode in enumerate(modes_to_include):\n",
    "        fs[m][i] = ee[m+1]-ee[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-23T16:20:52.124900Z",
     "start_time": "2019-08-23T16:20:51.950900Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Transition frequencies (GHz))')"
      ]
     },
     "execution_count": 7,
     "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": [
    "# Plot the eigenfrequencies\n",
    "plt.plot(phi_list,fs[0]/1e9)\n",
    "plt.plot(phi_list,fs[1]/1e9)\n",
    "plt.xlabel('Flux (flux quanta)')\n",
    "plt.ylabel('Transition frequencies (GHz))')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that we have constructed a Hamiltonian with modes 1 and 2, excluding mode 0, which corresponds to oscillations of current majoritarily located in the tuneable coupler.\n",
    "One can verify this fact by plotting the distribution of currents for mode 0 using the `show_normal_mode` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-23T16:20:52.539900Z",
     "start_time": "2019-08-23T16:20:52.127900Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 792x411.84 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "TC.show_normal_mode(mode = 0, \n",
    "    quantity = 'current',\n",
    "    Lj=Lj(0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This experiment can be viewed as two \"bare\" transmon qubits coupled by the interaction\n",
    "\n",
    "$\\hat H_\\text{int} = g\\sigma_x^L\\sigma_x^R$\n",
    "\n",
    "where left and right transmons are labeled $L$ and $R$ and $\\sigma_x$ is the $x$ Pauli operator.\n",
    "The coupling strength $g$ reflects the rate at which the two transmons can exchange quanta of energy.\n",
    "If the transmons are resonant a spectroscopy experiment reveals a hybridization of the two qubits, which manifests as two spectroscopic absorption peaks separated in frequency by $2g$.\n",
    "From this point of view, this experiment thus implements a coupling which is tuneable from an appreciable value to near 0 coupling."
   ]
  }
 ],
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