examples/demo_cos2phi_qubit.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# scqubits example: cos2phi qubit\n",
    "J. Koch and P. Groszkowski <br>Xinyuan You\n",
    "\n",
    "For further documentation of scqubits see https://scqubits.readthedocs.io/en/latest/.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-11T02:42:35.772716Z",
     "start_time": "2021-03-11T02:42:34.370047Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "\n",
    "import numpy as np\n",
    "import scqubits as scq"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# cos2phi qubit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$H = 2 E_\\text{CJ}'n_\\phi^2 + 2 E_\\text{CJ}' (n_\\theta - n_\\text{g} - n_\\zeta)^2 + 4 E_\\text{C} n_\\zeta^2\n",
    "         + E_\\text{L}'(\\phi - \\pi\\Phi_\\text{ext}/\\Phi_0)^2 + E_\\text{L}' \\zeta^2 - 2 E_\\text{J}\\cos{\\theta}\\cos{\\phi} \\\\\n",
    "         + 2 dE_\\text{J} E_\\text{J}\\sin{\\theta}\\sin{\\phi} \n",
    "         - 4 dC_\\text{J} E_\\text{CJ}' n_\\phi (n_\\theta - n_\\text{g}-n_\\zeta) \n",
    "         + dL E_\\text{L}'(2\\phi - \\varphi_\\text{ext})\\zeta,$\n",
    "         \n",
    "where $E_\\text{CJ}' = E_\\text{CJ} / (1 - dC_\\text{J})^2$ and $E_\\text{L}' = E_\\text{L} / (1 - dL)^2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To numerically diagonalize the Hamiltonian of the cos2phi qubit, the harmonic basis is used for both the $\\phi$ and $\\zeta$ variables, and the charge basis is used for the $\\theta$ variable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With ipywidgets installed, a cos2phi qubit instance can be created with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-11T02:42:35.969228Z",
     "start_time": "2021-03-11T02:42:35.775838Z"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b26d8450254647faac16b41bcdb158a8",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Row(children=[Row(children=[ValidatedNumberField(class_='ml-2 py-0', dense=True, error=False, filled=True, lab…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cos2phi_qubit = scq.Cos2PhiQubit.create()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternativley, the qubit instance can be crated with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-11T02:42:35.974074Z",
     "start_time": "2021-03-11T02:42:35.970941Z"
    }
   },
   "outputs": [],
   "source": [
    "cos2phi_qubit = scq.Cos2PhiQubit(EJ = 15.0,\n",
    "                                 ECJ = 2.0,\n",
    "                                 EL = 1.0,\n",
    "                                 EC = 0.04,\n",
    "                                 dCJ = 0.0,\n",
    "                                 dL = 0.6,\n",
    "                                 dEJ = 0.0,\n",
    "                                 flux = 0.5,\n",
    "                                 ng = 0.0,\n",
    "                                 ncut = 7,\n",
    "                                 phi_cut = 7,\n",
    "                                 zeta_cut = 30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-11T02:42:35.978143Z",
     "start_time": "2021-03-11T02:42:35.976060Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cos2PhiQubit--------| [Cos2PhiQubit_2]\n",
      "                    | EJ: 15.0\n",
      "                    | ECJ: 2.0\n",
      "                    | EL: 1.0\n",
      "                    | EC: 0.04\n",
      "                    | dCJ: 0.0\n",
      "                    | dL: 0.6\n",
      "                    | dEJ: 0.0\n",
      "                    | flux: 0.5\n",
      "                    | ng: 0.0\n",
      "                    | ncut: 7\n",
      "                    | zeta_cut: 30\n",
      "                    | phi_cut: 7\n",
      "                    |\n",
      "                    | dim: 3150\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(cos2phi_qubit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Potential energy\n",
    "evaluated by setting $\\zeta=0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-11T02:42:36.374414Z",
     "start_time": "2021-03-11T02:42:35.979646Z"
    }
   },
   "outputs": [
    {
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       "<Figure size 800x200 with 2 Axes>"
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     "metadata": {},
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   ],
   "source": [
    "cos2phi_qubit.plot_potential();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Eigenenergies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-11T02:42:36.379429Z",
     "start_time": "2021-03-11T02:42:36.377317Z"
    }
   },
   "outputs": [],
   "source": [
    "cos2phi_qubit.dL = 0.0\n",
    "cos2phi_qubit.n_cut = 10\n",
    "cos2phi_qubit.phi_cut = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-11T02:42:37.044824Z",
     "start_time": "2021-03-11T02:42:36.381092Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([15.03654563, 15.03691504, 15.80061319, 15.80464118, 16.56008481,\n",
       "       16.57785469, 17.3185442 , 17.35692015, 18.09641178, 18.12990415])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cos2phi_qubit.eigenvals(evals_count=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-11T02:43:37.024841Z",
     "start_time": "2021-03-11T02:42:37.046396Z"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e206c912aa12401eb52f074b9a040d13",
       "version_major": 2,
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      },
      "text/plain": [
       "Spectral data:   0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "flux_list = np.linspace(0, 0.6, 100)\n",
    "cos2phi_qubit.plot_evals_vs_paramvals('flux', flux_list, evals_count=14, subtract_ground=True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-11T02:43:38.389641Z",
     "start_time": "2021-03-11T02:43:37.026537Z"
    }
   },
   "outputs": [],
   "source": [
    "fig, ax = cos2phi_qubit.plot_wavefunction(which=0, mode='real', zero_calibrate=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-11T02:43:39.832466Z",
     "start_time": "2021-03-11T02:43:38.391435Z"
    }
   },
   "outputs": [],
   "source": [
    "fig, ax = cos2phi_qubit.plot_wavefunction(which=1, mode='real', zero_calibrate=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Matrix element"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-11T02:43:41.204625Z",
     "start_time": "2021-03-11T02:43:39.834124Z"
    }
   },
   "outputs": [],
   "source": [
    "cos2phi_qubit.plot_matrixelements('n_phi_operator', evals_count=10);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2021-03-11T02:42:34.385Z"
    }
   },
   "outputs": [],
   "source": [
    "flux_list = np.linspace(0.4, 0.6, 101)\n",
    "fig, ax = cos2phi_qubit.plot_matelem_vs_paramvals('n_phi_operator', 'flux', flux_list, select_elems=4);"
   ]
  }
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